J. L. Austin, in "Ifs and Cans," proclaimed the common hope that we soon "may see the birth, through the joint labors of philosophers, grammarians, and numerous other students of language, of a true and comprehensive science of language." The problem has always been with the "joint labors" part. Philosophers have always been willing to issue linguists dictums and linguists have been happy to teach philosophers "plain facts." Austin’s general view of language, and his particular notion of performative utterance, can (...) be found in the writing of J. R. Firth, the most commanding British linguist of Austin’s generation, but Austin never refers to Firth. In the present volume, however, we find clear and exciting evidence of genuinely joint labors on the part of philosophers and linguists. They stem from a summer conference in 1969 rounded out with contributions from notables. To two thick issues of Synthese the editors have added a dazzling piece by Saul Kripke, two substantial pieces by James McCawley and J. R. Ross, a short paper by Paul Ziff, and a reprint of P. F. Strawson’s "Grammar and Philosophy." This is an invaluable book and the best book among the many now available concerning the interaction of linguistics and philosophy: worth the cost, which the contributors attempted to reduce through foregoing royalties. The philosophers in this volume hold, or hold intriguing, the view that the semantics of a natural language can and must, in effect, be a theory of truth for a language in much the manner that Tarski suggested, and provided, for artificial language: the recursive specification of biconditionals in which the left hand gives the structural description of an object language sentence and the right hand, the truth conditions in the metalanguage. In "homophonic" translation this requirement can be trivially satisfied simply by mentioning the sentence on the left that one uses on the right: one makes the requirement non-trivial by forcing enough into the recursive specification so that one captures the native speaker’s implicit semantic competence. In this volume, the "orthodox" Davidsonian program, which takes the syntax of the metalanguage to be standard predicate logic, is ably argued by John Wallace ; Richard Montague, David Lewis, and Jaakko Hintikka would want an intensional logic covering modality and propositional attitudes. The linguists who find this philosophical climate most appealing are called "generative semanticists": McCawley, Ross, George Lakoff and others argue that any proposed semantic rule will eventually prove necessary to syntax too and that, hence, the deepest level of syntactical form will be equivalent to semantic form. Whatever the ultimate fate of this joint program, it leads here to much exciting interaction between linguists and philosophers: linguists who welcome the machinery and conceptual standards of modern logic, and philosophers who try to grasp the specifics of crucial issues in recent linguistic theory. Even if Quine’s doubts, here sketched, and Chomsky’s currently unpublished more technical objections should be well-founded, nonetheless the joint labor will have been very much worthwhile. Aside from this general debate about semantics, there are several papers covering more specific issues. The papers of J. A. Fodor, Terence Parsons, and Ross concern adverbs and the logical form of action sentences; several papers, particularly B. H. Partee’s, examine "Opacity, Coreference, and Pronouns." In all these papers one notes the fulfillment of Austin’s hope that philosophic and linguistic arguments should become intermixed, if not at times properly indistinguishable. Perhaps the most enjoyable and exciting paper stands aside from linguistics: Saul Kripke’s "Naming and Necessity." Kripke here argues quite informally for the separation of analytic, a priori, and necessary that is required for a Kripke style, S5, modal logic with de re modalities. "Gold is a yellow metal," for example, turns out to be contingent, while "Heat is the motion of particles" is necessary but a posteriori ; and that philosopher’s stone of stones, "The morning star is the evening star," is discovered to be necessary but a posteriori.—J. L. (shrink)

This extended investigation of the semantics of event (and state) sentences in their various forms is a major contribution to the semantics of natural language, simultaneously encompassing important issues in linguistics, philosophy, and logic. It develops the view that the logical forms of simple English sentences typically contain quantification over events or states and shows how this view can account for a wide variety of semantic phenomena. Focusing on the structure of meaning in English sentences (...) at a &"subatomic&" level&-that is, a level below the one most theories accept as basic or &"atomic&"&-Parsons asserts that the semantics of simple English sentences require logical forms somewhat more complex than is normally assumed in natural language semantics. His articulation of underlying event theory explains a wide variety of apparently diverse semantic characteristics of natural language, and his development of the theory shows the importance of seeing the distinction between events and states. Parsons demonstrates that verbs, also, indicate kinds of actions rather than specific, individual actions. Verb phrases, too, he argues, depend on modifiers to make their function and meaning in a sentence specific. An appendix gives many of the details needed to formalize the theory discussed in the body of the text and provides a series of templates that permit the generation of atomic formulas of English. (shrink)

This is primarily a conceptual paper. The goal of the paper is to put into perspective the proof-theory of hybrid logic and in particular, try to give an answer to the following question: Why does the proof-theory of hybrid logic work so well compared to the proof-theory of ordinary modal logic?Roughly, there are two different kinds of proof systems for modal logic: Systems where the formulas involved in the rules are formulas (...) of the object language, that is, ordinary modal-logical formulas, and systems where the formulas involved in the rules are metalingustic formulas obtained by attaching labels representing possible worlds to ordinary modal-logical formulas. Systems of the second kind often also involve an explicit representation of the accessibility relation. From a proof-theoretic point of view, modal-logical systems of the first kind are less well-behaved than systems of the second kind.It turns out that this can be remedied by hybridization, that is, hybridization of modal logics enables the formulation of well-behaved proof systems without involving metalinguistic machinery. What has happened is that the metalinguistic machinery has been internalized in the object language. This gives an answer to the initial question, which is that the proof-theory of hybrid logic works so well because the metalinguistic semantic machinery has been internalized in the object language. (shrink)

In this paper, we study three representations of lattices by means of a set with a binary relation of compatibility in the tradition of Ploščica. The standard representations of complete ortholattices and complete perfect Heyting algebras drop out as special cases of the first representation, while the second covers arbitrary complete lattices, as well as complete lattices equipped with a negation we call a protocomplementation. The third topological representation is a variant of that of Craig, Haviar, and Priestley. We then (...) extend each of the three representations to lattices with a multiplicative unary modality; the representing structures, like so-called graph-based frames, add a second relation of accessibility interacting with compatibility. The three representations generalize possibility semantics for classical modal logics to non-classical modal logics, motivated by a recent application of modal orthologic to natural language semantics. (shrink)

Frege's invention of the predicate calculus has been the most influential event in the history of modern logic. The calculus’ place in logic is so central that many philosophers think, in fact, of it when they think of logic. This book challenges the position in contemporary logic and philosophy of language of the predicate calculus claiming that it is based on mistaken assumptions. Ben-Yami shows that the predicate calculus is different from natural language in (...) its fundamental semantic charac. (shrink)

In Pietroski ( 2018 ) a simple representation language called SMPL is introduced, construed as a hypothesis about core conceptual structure. The present work is a study of this system from a logical perspective. In addition to establishing a completeness result and a complexity characterization for reasoning in the system, we also pinpoint its expressive limits, in particular showing that the fourth corner in the square of opposition (“ Some_not ”) eludes expression. We then study a seemingly small extension, (...) called SMPL +, which allows for a minimal predicate-binding operator. Perhaps surprisingly, the resulting system is shown to encode precisely the concepts expressible in first-order logic. However, unlike the latter class, the class of SMPL + expressions admits a simple procedural (context-free) characterization. Our contribution brings together research strands in logic—including natural logic, modal logic, description logic, and hybrid logic—with recent advances in semantics and philosophy of language. (shrink)

We study hybrid logics in topological semantics. We prove that hybrid logics of separation axioms are complete with respect to certain classes of finite topological models. This characterisation allows us to obtain several further results. We prove that aforementioned logics are decidable and PSPACE-complete, the logics of T 1 and T 2 coincide, the logic of T 1 is complete with respect to two concrete structures: the Cantor space and the rational numbers.

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 9.2 (2002) 127-129 [Access article in PDF] Linguistic Markers of Recovery:Underpinnings of First Person Pronoun Usage and Semantic Positions of Patients Patrick Suppes Keywords: association, freedom, habits, psychotherapy, roles, semantics. USING LINGUISTIC EVIDENCE to evaluate recovering psychotherapy patients is an attractive and useful idea. I agree with much of Dr. van Staden's proposals for doing so. The purpose of this commentary is to give (...) some comments and criticisms on points of detail. Roles, Not Semantics A fair amount of Dr. van Staden's article is concerned with the semantics of relations. The focus on relations is a good thing. Restricting discourse about patients to properties is not sufficient, for everyone regards how a person is relating to others, and even to other things, as an important feature of normal behavior and mental health. We do not want just to report, "John was upset," but consider it definitely more informative to say, "John was upset by his father's criticisms." The English language and all other natural languages are rich in verbs for expressing relations with emotional affect between two or more persons, or a person and an event or thing. Staden's article focuses on the interesting and important case of first person pronouns. To go from saying, "She made me do it" to "I did it" is, for reasons that need not be spelled out, a sign of progress. A way to describe this change is that the speaker has indicated that in the implicit context assumed he or she has shown signs of moving from the role of being a patient to that of being an actor, from being a recipient of actions to being a performer of acts.van Staden concentrates on the semantics of relations to bring out what I call the change of roles. I would certainly agree that such change of roles is important to the semantics of affective or action verbs and verb phrases. We have no disagreement at all about this. Yet I am critical of his wanting to range much wider in his analysis of semantics. The logical or formal treatment of relations is a large topic, full of many distinctions and subtleties that seem to me not too relevant to his main theme. In a very general way he wants to say that what is usually thought of as [End Page 127] the first position in a relation, what he calls the alpha position, is occupied by the owner of the relation, and the second position, in a binary relation—the main case discussed—is occupied by the accidental to that particular relation. This second position is called the omega position.This runs contrary to much of the mathematical literature on relations, which occupy an important place in many parts of mathematics such as geometry. So when we say that one triangle is larger than another, it seems positively weird to say the second triangle is somehow accidental to the relation. But this is true and confusing even for the familiar and classical kinds of actions often cited by van Staden. In analyzing the sentence "Brutus killed Caesar intentionally" it sounds really strange to say that Caesar occupied the accidental position in the expressed relation of killing.Moreover, in the conceptual and philosophical discussion of relations, it is common practice to stress that even if the natural grammar of a sentence has a subject-predicate structure, as in "Elizabeth is the mother of Charles," no special logical force is given to what van Staden calls the first or alpha position in most mathematical relations, such as "The number 2 is less than the number 3," expressed in ordinary mathematical notation as "2 < 3."On the other hand, I stress that it is natural to distinguish in a relational sentence expressing an action between the role of actor and the role of patient, no matter which is the grammatical subject of the sentence, as in the following pair "John hurt Mary" and "Mary was hurt by John." The roles of actor... (shrink)

Introduction. PHilosophy of Language and Linguistics: The Formal Turn Piotr Stalmaszczyk Gottlob Frege, Philosophy of Language, and Predication Piotr Stalmaszczyk Philosophy, Linguistics and Semantic Interpretation Christian Bassac An Unresolved Issue: Nonsense in Natural Language and Non-Classical Logical and Semantic Systems Elzbieta Chrzanowska-Kluczewska Varieties of Context-Dependence Tadeusz Ciecierski The Logos of Semantic Structure Marie Du í, Bjørn Jespersen and Pavel Materna The Good Samaritan and the Hygienic Cook: A Cautionary Tale About Linguistic Data Chris Fox The Meaning of Multiple Quantified (...) Sentences: Where Formal Semantics Meets Psycholinguistics Justyna Grudzinska The Hybrid Theory of Reference for Proper Names Filip Kawczynski On the Nature of Statistical Language Laws Agnieszka Kulacka Vagueness and Contextualism Joanna Odrowaz-Sypniewska The Myth of Semantic Structure Jaroslav Peregrin Scalar Implicatures, Communication and Language Evolution Salvatore Pistoia Reda Semantics and Contextuality: The Case of Pia s Leaves Stefano Predelli Is Logico-Semantical Analysis of Natural Language Expressions a Translation? Jirí Raclavský Beyond the Fregean Myth: The Value of Logical Values Fabien Schang Modal Calculus of Illocutionary Logic Andrew Schumann Subjectivity in Philosophy and Linguistics Barbara Sonnenhauser Asymmetrical Semantics Mieszko Talasiewicz Truth: An Anti-realist Adequacy Condition Luca Tranchini Belief Reports: Defaults, Intentions and Scorekeeping Giacomo Turbanti On Truth in Time Bartosz Wieckowski Order William J. SUllivan Indexes. (shrink)

It is now a quarter of a century ago that Wolfgang Stegmfiller wrote his monograph 'Das Wahrheitsproblem und die Idee der Semantik' (1957) which dealt with Tarski's and Carnap's foundational work in the field of semantics. While this book is about the definition of the basic semantical concepts in artificial formal languages there is an article written a year earlier (1956) in which Stegmfiller addresses himself specifically to the relation between logic and natural language. Here he gives (...) a logical analysis of the standard structural expressions in language that are still of primary concern for current semantics: quantifiers, pronouns, articles, etc. The motives for such an analysis at that time were mainly philosophical: the aim was to expose the misconceptions and pitfalls of traditional philosophy arising from the disregard of various systematic semantic ambiguities in everyday language. Or as Stegmfiller puts it: Ober sie [i.e. einige nicht triviale F~ille von Vagheit in der A11tagssprache] Klarheit zu gewinnen, ist schon deshalb yon auBerordentlicher Bedeutung, weil Unkenntnis fiber sie zu schwersten philosophischen Verirrungen ffihren kann, namlich entweder der Unterlassung von berechtigten Fragestellungen, oder, was weit h~ufiger vorgekommen ist, der Formulierung yon falsch gestellten Fragen, denen gegenfiber man dann nur die Wahl hat, entweder fiberhaupt keine oder nur sinnlose Antworten zu geben. So logic was to regiment language. Sentences involving the copula and the above-mentioned structure words are assigned one or more unambiguous formal representations in an already interpreted formal language, usually the first order predicate calculus. The natural language expressions thereby receive a precise meaning, since the semantics of the formal language has been specified in advance, as is always assumed. This procedure has, of course, always been common practice, witness the typical syntactical argot of the mathematicians. It carries, however, an obvious methodological presupposition: it is the idea that the logic of our choice to which the formal representations belong is in some sense an adequate framework to express our thoughts. (shrink)

ABSTRACT: This chapter offers a revenge-free solution to the liar paradox (at the centre of which is the notion of Gestalt shift) and presents a formal representation of truth in, or for, a natural language like English, which proposes to show both why -- and how -- truth is coherent and how it appears to be incoherent, while preserving classical logic and most principles that some philosophers have taken to be central to the concept of truth and our (...) use of that notion. The chapter argues that, by using a truth operator rather than truth predicate, it is possible to provide a coherent, model-theoretic representation of truth with various desirable features. After investigating what features of liar sentences are responsible for their paradoxicality, the chapter identifies the logic as the normal modal logic KT4M (= S4M). Drawing on the structure of KT4M (=S4M), the author proposes that, pace deflationism, truth has content, that the content of truth is bivalence, and that the notions of both truth and bivalence are semideterminable. (shrink)

Objective. Conceptualization of the definition of space as a semantic unit of language consciousness. -/- Materials & Methods. A structural-ontological approach is used in the work, the methodology of which has been tested and applied in order to analyze the subject matter area of psychology, psycholinguistics and other social sciences, as well as in interdisciplinary studies of complex systems. Mathematical representations of space as a set of parallel series of events (Alexandrov) were used as the initial theoretical basis of the (...) structural-ontological analysis. In this case, understanding of an event was considered in the context of the definition adopted in computer science – a change in the object properties registered by the observer. -/- Results. The negative nature of space realizes itself in the subject-object structure, the components interaction of which is characterized by a change – a key property of the system under study. Observer’s registration of changes is accompanied by spatial focusing (situational concretization of the field of changes) and relating of its results with the field of potentially distinguishable changes (subjective knowledge about «changing world»). The indicated correlation performs the function of space identification in terms of recognizing its properties and their subjective significance, depending on the features of the observer`s motivational sphere. As a result, the correction of the actual affective dynamics of the observer is carried out, which structures the current perception of space according to principle of the semantic fractal. Fractalization is a formation of such a subjective perception of space, which supposes the establishment of semantic accordance between the situational field of changes, on the one hand, and the worldview, as well as the motivational characteristics of the observer, on the other. -/- Conclusions. Performed structural-ontological analysis of the system formed by the interaction of the perceptual function of the psyche and the semantic field of the language made it possible to conceptualize the space as a field of changes potentially distinguishable by the observer, structurally organized according to the principle of the semantic fractal. The compositional features of the fractalization process consist in fact that the semantic fractal of space is relevant to the product of the difference between the situational field of changes and the field of potentially distinguishable changes, adjusted by the current configuration of the observer`s value-needs hierarchy and reduced by his actual affective dynamics. (shrink)

Approaches to anaphora generally seek to explain the potential for a DP to covary with a pronoun in terms of a combination of factors, such as the inherent semantics of the antecedent DP, its scope properties, and its structural position. A case in point is Reinhart’s classic condition on bound anaphora, paraphrasable as A DP can antecede a pronoun pro only if the DP c-commands pro at S-structure, supplemented with some extra machinery to allow indefinites to covary with pronouns (...) beyond their c-command domains. In the present paper, I explore a different take. I propose that anaphora is governed not by DPs and their properties; it is governed by predicates and their properties. To use a metaphor from dynamic semantics: discourse referents can only be ‘activated’ by predicates, never by DPs. This conceptually simple assumption is shown to have far-reaching consequences. For one, it yields a new take on weak crossover, arguably worthy of consideration. Moreover, it leads to a further general “restatement of the anaphora question”, in Reinhart’s words. (shrink)

Modal Logic, originally conceived as the logic of necessity and possibility, has developed into a powerful mathematical and computational discipline. It is the main source of formal languages aimed at analyzing complex notions such as common knowledge and formal provability. Modal and modal-like languages also provide us with families of restricted description languages for relational and topological structures; they are being used in many disciplines, ranging from artificial intelligence, computer science and mathematics via natural (...) language syntax and semantics to philosophy. This volume presents a broad and up-to-date view of the field, with contributions covering both the foundations of modal logic itself and each of the aforementioned application areas. Complemented with an editorial introduction covering the roots of modal logic, this book is indispensable for any advanced student and researcher in non-classical logic and its applications. (shrink)

The investigation is devoted to the problem of formal representation of logical structure and ontological commitments of natural language event sentences. The specificity of ontological commitments problem with regard to natural and formal languages is shown. The alternative approaches to the formal representation of event sentences (argument approach, davidsonian and neodavidsonian approaches, operator approach) are characterized with respect to their key features from formal logical and ontological points of view. The difference in the logical structure of (...) sentences expressing events by verb phrases and by nominalization is depicted. The role of a paraphrase in formal representation of natural language phenomena is discussed, as well as the notions of “hermeneutic" and “revolutionary" approaches in logic-semantical analysis introduced by J. Burgess and G. Rosen. It is shown that the neodavidsonian approach with regard to verb phrases is an example of “revolutionary" approach because it changes the original logical structure of natural language sentences. The analysis of ontological commitments shows that there is no bound event variable in the logical structure of verb phrases at sentence level but it's included in the internal semantic structure of a verb. The possible ways to the logical interpretation of the natural language mechanism of the dynamic shift between verb-based and nomi- nalized sentences are outlined. (shrink)

In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally (...) a non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Fariñas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum–Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum–Tarski algebras. (shrink)

The book defines the concept of Semantic-Communicative Structure [= Sem-CommS]-a formal object that is imposed on the starting Semantic Structure [= SemS] of a sentence (under text synthesis) in order to turn the selected meaning into a linguistic message. The Sem-CommS is a system of eight logically independent oppositions: 1. Thematicity (Rheme vs. Theme), 2. Givenness (Given vs. Old), 3. Focalization (Focalized vs. Non-Focalized), 4. Perspective (Foregrounded vs. Backgrounded), 5. Emphasis (Emphasized vs. Non-Emphasized), 6. Presupposedness (Presupposed vs. Non-Presupposed), 7. Unitariness (...) (Unitary vs. Articulated), 8. Locutionality (Communicated vs. Signaled). The values of these oppositions mark particular subnetworks of the starting SemS and thus allow for the distinction between sentences such as (a) A man killed a dog vs. The dog was killed by a man, (b) John washed the window vs. It was John who washed the window or (c) It hurts! vs. Ouch! The proposed Sem-Comm-oppositions are conceived as an attempt at sharpening the well-known notions of Topic Comment, Focus, etc. Possible linguistic strategies for expressing the values of the Sem-Comm-oppositions in different languages are discussed at some length, with linguistic illustrations. (shrink)

Event semantics is concerned with the formal structure of sentences which appear to describe an event of some kind, e.g. ‘Brutus kills Caesar,’ or ‘My tooth fell out.’ Phenomenologists should be interested in work in this field, if they hope to rescue Husserl’s phenomenology of judgment from its narrow focus on copular judgments of the form ‘S is p.’ An adequate phenomenology of judgment must ultimately develop an account of judgments whose intentional correlates seem to be events, (...) rather than states of affairs, since such judgments are ubiquitous. For this endeavor, existing work on the formal structure of event sentences provides a crucial foothold. However, phenomenologists cannot simply import semantic theories for their own use, without first evaluating them for phenomenological plausibility. This concern is particularly acute in the case of the widely-adopted “Davidsonian” approach, according to which the logical structure of event sentences diverges radically from natural language syntax. The Davidsonian form introduces a “covert” variable, which stands in for an event. Thus, the sentence ‘Brutus kills Caesar’ becomes, ‘There is an event e that is a killing of Caesar by Brutus.’ Such a theory, if correct, would have decisive consequences for the phenomenology of event sentences, and even of events themselves. Yet the introduction of covert variables in turn introduces—I argue—a covert intentional object, without assessing this idea for phenomenological plausibility. Building on Husserl’s phenomenology of predication, I develop a criterion for evaluating this hypothesis, and argue that the Davidsonian approach, as it stands, is phenomenologically untenable. (shrink)

Description Logics (DLs) are a family of well-known terminological knowledge representation formalisms in modern semantics-based systems. This research focuses on analysing how our developed Occurrence Logic (OccL) can conceptually and logically support the development of a description logic. OccL is integrated into the alternative theory of natural language syntax in `Deviational Syntactic Structures' under the label `EFA(X)3' (or the third version of Epi-Formal Analysis in Syntax, EFA(X), which is a radical linguistic theory). From the logical point (...) of view, OccL is a formal logic that mainly deals with the occurrences of symbols as well as with their priorities within linguistic descriptions, i.e. natural language syntax, semantics and phonology. In this article---based on our OccL-based definitions of the concepts of `strong implication' and `occurrence value' as well as of the logical concept `identical occurrence constructor (IDOC)' that is the most fundamental logical concept in our formalism---we will model Occurrence Description Logic ($\mathcal{ODL}$). Accordingly, we will formally-logically analyse `occurrence(s) of symbol(s)' within descriptions of the world in $\mathcal{ODL}$. In addition, we will analyse and assess the logical concepts of `occurrence' and `occurrence priority' in $\mathcal{ODL}$. This research can make a strong logical background for our future research in the development of a Modal Occurrence Description Logic. (shrink)

This paper deals with structures ${\langle{\bf T}, I\rangle}$ in which T is a tree and I is a function assigning each moment a partition of the set of histories passing through it. The function I is called indistinguishability and generalizes the notion of undividedness. Belnap’s choices are particular indistinguishability functions. Structures ${\langle{\bf T}, I\rangle}$ provide a semantics for a language ${\mathcal{L}}$ with tense and modal operators. The first part of the paper investigates the set-theoretical properties of the set (...) of indistinguishability classes, which has a tree structure. The significant relations between this tree and T are established within a general theory of trees. The aim of second part is testing the expressive power of the language ${\mathcal{L}}$ . The natural environment for this kind of investigations is Belnap’s seeing to it that (stit). It will be proved that the hybrid extension of ${\mathcal{L}}$ (with a simultaneity operator) is suitable for expressing stit concepts in a purely temporal language. (shrink)

In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a (...) nice topological interpretation. This constitutes a new proof of S4 as being "the logic of topological spaces", but now under the perspective of paraconsistency. (shrink)

We describe a knowledge representation and inference formalism, based on an intensional propositional semantic network, in which variables are structures terms consisting of quantifier, type, and other information. This has three important consequences for natural language processing. First, this leads to an extended, more natural formalism whose use and representations are consistent with the use of variables in natural language in two ways: the structure of representations mirrors the structure of the language and allows re-use phenomena such (...) as pronouns and ellipsis. Second, the formalism allows the specification of description subsumption as a partial ordering on related concepts (variable nodes in a semantic network) that relates more general concepts to more specific instances of that concept, as is done in language. Finally, this structured variable representation simplifies the resolution of some representational difficulties with certain classes of natural language sentences, namely, donkey sentences and sentences involving branching quantifiers. The implementation of this formalism is called ANALOG (A NAtural LOGIC) and its utility for natural language processing tasks is illustrated. (shrink)

This book addresses two related questions that have first arisen in Toulmin’s seminal book on the uses of argument. The first question is the one of the relationship between the semantic analysis of modality and the structure of arguments. The second question is the one of the distinctive place, or role, of modality in the fundamental structure of arguments. These two questions concern how modality, as a semantic category, relates to the fundamental structure of arguments. The book addresses modality and (...) argumentation also according to another perspective by looking at how different linguistic modal expressions may be taken as argumentative indicators. It explores the role of modal expressions as argumentative indicators by using the Italian modal system as a case study. At the same time, it uses predictions/forecasts in the business-financial daily press to investigate the relation between modality and the context of argumentation. (shrink)

We started from the fact that type theory, in the way it was implemented in IL, makes it costly to deal with nominalization processes. We have also argued that the type hierarchy as such doesn't play any real role in a grammar; the classification it provides for different semantic objects is already contained, in some sense, in the categorial structure of the grammar itself. So, on the basis of a theory of properties (Cocchiarella's HST*) we have tried to build a (...) language (IL*) whose syntax does not contain any explicit typing of expressions. Some of the consequences that this move brings about in the overall organization of the grammar can be summarized as follows:it allows for a simple treatment of infinitives, gerunds, factives and, in general, all those phenomena which might be analyzed as cases of nominalization;it provides a simpler and more constrained semantics than IL, since IL* doesn't go beyond second order, and its non-modal basis is axiomatizable;it suggests that the role of logical form in a theory of grammar could be that of a family of theories of semantic objects;it eliminates the extrinsic limitations of a type hierarchy on the choice of the system of syntactic categories.I think that it is interesting to notice how having an explicit semantic framework helps to provide a sense in which it is legitimate to regard the syntax of a language as ‘autonomous’. (shrink)

The problem of semantic closedness of natural, or colloquial, languages presupposes the investigation of the entire class of their essential semantic properties rather than that of individual instances. To be more concrete, the properties involved are those of universality, antinomisity, and the lack of strict distinction between language and metalanguage. There are reasons to believe that those properties in their totality constitute what underlies the structural unity and functional completeness of natural languages as exceptionally complex informational-communicative systems.

Is medieval logic formal? And if yes, in what sense? There are striking affinities between medieval and contemporary theories of language. Authors from the two periods share formal ambitions and maintain complex, and at time uneasy, relations with natural language. However, modern scholars became careful not to overlook the specificities of theories developed more than five hundred years apart, in particular with respect to their 'formal' character. In 1972, Alfonso Maieru noted that the efforts of medieval logicians to (...) identify logical structures in language formal enough to become objects of scientific consideration. He also stressed that the language investigated is a historical one, Latin, so that one can legitimately wonder to which extent... one is allowed to speak of 'formal logic' in the middle ages. In other words, medieval logic is characterized by a tension between 'formalist ambitions' and constraints proper to natural language. Today, our knowledge of the field has considerably expanded, calling for a new assessment of the question. (shrink)

Mental Spaces is the classic introduction to the study of mental spaces and conceptual projection, as revealed through the structure and use of language. It examines in detail the dynamic construction of connected domains as discourse unfolds. The discovery of mental space organization has modified our conception of language and thought: powerful and uniform accounts of superficially disparate phenomena have become available in the areas of reference, presupposition projection, counterfactual and analogical reasoning, metaphor and metonymy, and time and aspect (...) in discourse. The present work lays the foundation for this research. It uncovers simple and general principles that lie behind the awesome complexity of everyday logic. (shrink)

Preface This book is about semantics and logic. More specifically, it is about the semantics and logic of natural language; and, even more specifically than ...

Before presenting the analysis of logical form of questions, I shall make some comments concerning questions in natural language. By utilizing examples of such questions I shall try to justify my conception of the semiotic function of questions and provide a basis for my analysis of their structure. One of the main aims of this chapter is to introduce definitions of erotetic concepts which I will use in the subsequent parts of the book and to sketch definitional connections between (...) elements of the erotetic conceptual scheme. (shrink)

This essay aims to provide a modal logic for rational intuition. Similarly to treatments of the property of knowledge in epistemic logic, I argue that rational intuition can be codified by a modal operator governed by the modal $\mu$-calculus. Via correspondence results between fixed point modal propositional logic and the bisimulation-invariant fragment of monadic second-order logic, a precise translation can then be provided between the notion of 'intuition-of', i.e., the cognitive phenomenal properties (...) of thoughts, and the modal operators regimenting the notion of 'intuition-that'. I argue that intuition-that can further be shown to entrain conceptual elucidation, by way of figuring as a dynamic-interpretational modality which induces the reinterpretation of both domains of quantification and the intensions and hyperintensions of mathematical concepts that are formalizable in monadic first- and second-order formal languages. Hyperintensionality is countenanced via a topic-sensitive epistemic two-dimensional truthmaker semantics. (shrink)

In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language (a decidable system with the same complexity as orthodox propositional modal logic) to the strong Priorean language (which offers full first-order expressivity).We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it (...) is possible to define base logics which extend automatically to a wide variety of frame classes and to prove completeness using the Henkin method. In the weaker languages, this requires the use of non-orthodox rules. We discuss these rules in detail and prove non-eliminability and eliminability results. We also show how another type of rule, which reflects the structure of the strong Priorean language, can be employed to give an even wider coverage of frame classes. We show that this deductive apparatus gets progressively simpler as we work our way up the expressivity hierarchy, and conclude the paper by showing that the approach transfers to first-order hybrid logic. (shrink)

Developed by Arthur Prior, Temporal Logic allows to represent temporal information on a logical system using modal operators such as P, F, H or G, whose intuitive meaning is “it was sometime in the Past...”, “it will be sometime in the Future...”, “it Has always been in the past...” and “it will always Going to be in the future...” respectively. Valuation of formulae built from these operators are carried out on Kripke semantics, so Modal Logic (...) and Temporal Logic are consequently related. In fact, Temporal Logic is an extension of Modal one. Even when both logics mechanisms are able to formalize modal-temporal information with some accuracy, they suffer from a lack of expressiveness which Hybrid Logic can solve. Indeed, one of the problems of Modal Logic consists in its incapacity of naming specific points inside a model. As Temporal Logic is based on it, it cannot make such a thing neither. But First-Order Logic does can by means of constants and equality relation. Hybrid Logic, which results from combining Modal Logic and First-Order Logic, may solve this shortcoming. The main aim of this paper is to explain how Hybrid Logic emanates from Modal and Temporal ones in order to show what it adds to both logics with regard to information representation, why it is more expressive than them and what relation it maintains with the First-Order Correspondence Language. (shrink)

Developed by Arthur Prior, Temporal Logic allows to represent temporal information on a logical system using modal operators such as P, F, H or G, whose intuitive meaning is “it was sometime in the Past...”, “it will be sometime in the Future...”, “it Has always been in the past...” and “it will always Going to be in the future...” respectively. Valuation of formulae built from these operators are carried out on Kripke semantics, so Modal Logic (...) and Temporal Logic are consequently related. In fact, Temporal Logic is an extension of Modal one. Even when both logics mechanisms are able to formalize modal-temporal information with some accuracy, they suffer from a lack of expressiveness which Hybrid Logic can solve. Indeed, one of the problems of Modal Logic consists in its incapacity of naming specific points inside a model. As Temporal Logic is based on it, it cannot make such a thing neither. But First-Order Logic does can by means of constants and equality relation. Hybrid Logic, which results from combining Modal Logic and First-Order Logic, may solve this shortcoming. The main aim of this paper is to explain how Hybrid Logic emanates from Modal and Temporal ones in order to show what it adds to both logics with regard to information representation, why it is more expressive than them and what relation it maintains with the First-Order Correspondence Language. (shrink)

In this dissertation we present proof systems for several modal logics. These proof systems are based on analytic (or semantic) tableaux. -/- Modal logics are logics for reasoning about possibility, knowledge, beliefs, preferences, and other modalities. Their semantics are almost always based on Saul Kripke’s possible world semantics. In Kripke semantics, models are represented by relational structures or, equivalently, labeled graphs. Syntactic formulas that express statements about knowledge and other modalities are evaluated in terms of (...) such models. -/- This dissertation focuses on modal logics with dynamic operators for public announcements, belief revision, preference upgrades, and so on. These operators are defined in terms of mathematical operations on Kripke models. Thus, for example, a belief revision operator in the syntax would correspond to a belief revision operation on models. -/- The ‘dynamic’ semantics of dynamic modal logics are a clever way of extending languages without compromising on intuitiveness. We present ‘dynamic’ tableau proof systems for these dynamic semantics, with the express aim to make them conceptually simple, easy to use, modular, and extensible. This we do by reflecting the semantics as closely as possible in the components of our tableau system. For instance, dynamic operations on Kripke models have counterpart dynamic relations between tableaux. -/- Soundness, completeness, and decidability are three of the most important properties that a proof system may have. A proof system is sound if and only if any formula for which a proof exists, is true in every model. A proof system is complete if and only if for any formula that is true in all models, a proof exists. A proof system is decidable if and only if any formula can be proved to be a theorem or not a theorem in a finite number of steps. All proof systems in this dissertation are sound, complete, and decidable. -/- Part of our strategy to create modular tableau systems is to delay concerns over decidability until after soundness and completeness have been established. Decidability is attained through the operations of folding and through operations on ‘tableau cascades’, which are graphs of tableaux. -/- Finally, we provide a proof-of-concept implementation of our dynamic tableau system for public announcement logic in the Clojure programming language. (shrink)

The hybrid logic and the independence friendly modal logic IFML are compared for their expressive powers. We introduce a logic IFML c having a non-standard syntax and a compositional semantics; in terms of this logic a syntactic fragment of IFML is singled out, denoted IFML c . (In the Appendix it is shown that the game-theoretic semantics of IFML c coincides with the compositional semantics of IFML c .) The hybrid (...) logic is proven to be strictly more expressive than IFML c . By contrast, and the full IFML are shown to be incomparable for their expressive powers. Building on earlier research (Tulenheimo and Sevenster 2006), a PSPACE -decidable fragment of the undecidable logic is disclosed. This fragment is not translatable into the hybrid logic and has not been studied previously in connection with hybrid logics. In the Appendix IFML c is shown to lack the property of ‘quasi-positionality’ but proven to enjoy the weaker property of ‘ bounded quasi-positionality’. The latter fact provides from the IFML internal perspective an account of what makes the compositional semantics of IFML c possible. (shrink)

The dissertation gives a second-order-logic-based explanation of modal incompleteness. The leading concept is that modal incompleteness is to be explained in terms of the incompleteness of standard second-order logic, since modal language is basically a second-order language. The development of Kripke-style semantics for modal logic has been underpinned by the conjecture that all modal systems are characterizable by classes of frames defined by first-order conditions on a binary relation. However, the discovery (...) of certain incomplete modal systems has undermined the all-encompassing feature of Kripke-style approach. There are logics not determined by any class of Kripke frames at all. ;In the dissertation I investigate a normal incomplete sentential modal system due to J. F. A. K. Van Benthem, and I address both the formal and the philosophical facets of modal incompleteness from the vantage point that modal logic is essentially second-order in its nature. Modal systems can be analyzed in terms of structures with a domain of second-order individuals that are assigned under an interpretation to propositional variables within languages of sentential modal logic. Hence, the phenomenon of there being incomplete modal systems can be accounted for through the incompleteness of standard second-order logic. ;Since second-order logic plays a crucial role in the explanation, Quine's animadversions upon second-order logic and in particular his views that second-order logic is 'Set Theory in Sheep's Clothing' are examined. Against Quine's stance I will seek to show that a vindication of second-order logic can be gotten provided a proper due is given to the sharp distinction between the logical notion of set which is the concern of second-order logic and the iterative notion of set which lies within the realm of set theory. (shrink)

This book develops a novel generalization of possible world semantics, called ‘world line semantics’, which recognizes worlds and links between world-bound objects (world lines) as mutually independent aspects of modal semantics. Addressing a wide range of questions vital for contemporary debates in logic and philosophy of language and offering new tools for theoretical linguistics and knowledge representation, the book proposes a radically new paradigm in modal semantics. This framework is motivated philosophically, viewing a (...) structure of world lines as a precondition of modal talk. The author provides a uniform analysis of quantification over individuals (physical objects) and objects of thought (intentional objects). The semantic account of what it means to speak of intentional objects throws new light on accounts of intentionality and singular thought in the philosophy of mind and offers novel insights into the semantics of intensional transitive verbs. (shrink)

This article contains the results of a theoretical analysis of the phenomenon of natural language understanding (NLU), as a methodological problem. The combination of structural-ontological and informational-psychological approaches provided an opportunity to describe the subject matter field of NLU, as a composite function of the mind, which systemically combines the verbal and discursive structural layers. In particular, the idea of NLU is presented, on the one hand, as the relation between the discourse of a specific speech message and the (...) meta-discourse of a language, in turn, activated by the need-motivational factors. On the other hand, it is conceptualized as a process with a specific structure of information metabolism, the study of which implies the necessity to differentiate the affective (emotional) and need-motivational influences on the NLU, as well as to take into account their interaction. At the same time, the hypothesis about the influence of needs on NLU under the scenario similar to the pattern of Yerkes-Dodson is argued. And the theoretical conclusion that emotions fulfill the function of the operator of the structural features of the information metabolism of NLU is substantiated. Thus, depending on the modality of emotions in the process of NLU, it was proposed to distinguish two scenarios for the implementation of information metabolism - reduction and synthetic. The argument in favor of the conclusion about the productive and constitutive role of emotions in the process of NLU is also given. (shrink)

This is a companion paper to Braüner where a natural deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the first-order case. Our natural deduction system for first-order hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by so-called geometric theories. We prove soundness and completeness and we prove a normalisation theorem. Moreover, we give (...) an axiom system first-order hybrid logic. (shrink)

This book pursues the question of how and whether natural language allows for reference to abstract objects in a fully systematic way. By making full use of contemporary linguistic semantics, it presents a much greater range of linguistic generalizations than has previously been taken into consideration in philosophical discussions, and it argues for an ontological picture is very different from that generally taken for granted by philosophers and semanticists alike. Reference to abstract objects such as properties, numbers, propositions, (...) and degrees is considerably more marginal than generally held. (shrink)

A volume of studies in natural language semantics which brings together work by philosophers, logicians and linguists. The main topics treated are: quantification and reference in natural language; the relations between formal logic, programming languages and natural language; pragmatics and discourse meaning; surface syntax and logical meaning. The volume derives from a colloquium organised in 1973 by the Kings College Research Centre, Cambridge and the papers have been edited for publication by Professor Keenan. It is (...) hoped that the collection will make available some of the best work in this fast-moving field and will stimulate further progress by juxtaposing the different approaches and interests represented here. (shrink)

Charles Chihara gives a thorough critical exposition of modal realism, the philosophical doctrine that there exist many possible worlds of which the actual world--the universe in which we live--is just one. The striking success of possible-worlds semantics in modal logic has made this ontological doctrine attractive. Modal realists maintain that philosophers must accept the existence of possible worlds if they wish to have the benefit of using possible-worlds semantics to assess modal arguments and (...) explain modal principles. Chihara challenges this claim, and argues instead for modality without worlds; he offers a new account of the role of interpretations or structures of the formal languages of logic. (shrink)

CHAPTER 1. INTENSIONAL LOGIC §1. Natural Language and Intensional Logic When we speak of a theory of meaning for a natural language such as English, ...

This paper gives an outline of truthmaker semantics for natural language against the background of standard possible-worlds semantics. It develops a truthmaker semantics for attitude reports and deontic modals based on an ontology of attitudinal and modal objects and on a semantic function of clauses as predicates of such objects. It also présents new motivations for 'object-based truthmaker semantics' from intensional transitive verbs such as ‘need’, ‘look for’, ‘own’, and ‘buy’ and gives an outline (...) of their semantics. This paper is a commissioned 'target' article, with commentaries by W. Davis, B. Arsenijevic, K. Moulton, K. Liefke, M. Kaufmann, R. Matthews, P. Portner and A. Rubinstein, P. Elliott, G. Ramchand and my reply. (shrink)

Artificial agents, which are embedded in a virtual world, need to interpret a sequence of commands given to them adequately, considering the temporal structure for each command. In this paper, we start with the semantics of natural language and classify the temporal structures of various eventualities into such aspectual classes as action, process, and event. In order to formalize these temporal structures, we adopt Arrow Logic. This logic specifies the domain for the valuation of a (...) sentence as an arrow. We can connect, or give order to, arrows by defining inter-arrow operations, and can give different views for sentences. Thereafter we formalize the rules of aspectual shifts in situated inference, in the style of a logic programming language. Thus, we not only describe the static representation of temporal features, but also show the dynamic process to deduce how each eventuality is viewed. The rules are applied to the information flow through the sequence of commands; therefore, we consider how the temporal structure of a command affects the succeeding commands. (shrink)

Progress in philosophy is difficult to achieve because our methods are evidentially and rhetorically weak. In the last two decades, experimental philosophers have begun to employ the methods of the social sciences to address philosophical questions. However, the adequacy of these methods has been called into question by repeated failures of replication. Experimental philosophers need to incorporate more robust methods to achieve a multi-modal perspective. In this chapter, we describe and showcase cutting-edge methods for data-mining and visualization. Big data (...) is a useful investigatory tool for moral psychology, and it fits well with the Ramsification method the first author advances in a series of recent papers. The guiding insight of these papers is that we can infer the meaning and structure of concepts from patterns of assertions and inferential associations in natural language. (shrink)

Charles Chihara gives a thorough critical exposition of modal realism, the philosophical doctrine that there exist many possible worlds of which the actual world--the universe in which we live--is just one. The striking success of possible-worlds semantics in modal logic has made thisontological doctrine attractive. Modal realists maintain that philosophers must accept the existence of possible worlds if they wish to have the benefit of using possible-worlds semantics to assess modal arguments and explain (...) modal principles. Chihara challenges this claim, and argues instead formodality without worlds; he offers a new account of the role of interpretations or structures of the formal languages of logic. (shrink)

We propose an approach to natural language inference based on a model of natural logic, which identifies valid inferences by their lexical and syntactic features, without full semantic interpretation. We greatly extend past work in natural logic, which has focused solely on semantic containment and monotonicity, to incorporate both semantic exclusion and implicativity. Our system decomposes an inference problem into a sequence of atomic edits linking premise to hypothesis; predicts a lexical entailment relation for each (...) edit using a statistical classifier; propagates these relations upward through a syntax tree according to semantic properties of intermediate nodes; and composes the resulting entailment relations across the edit sequence. We evaluate our system on the FraCaS test suite, and achieve a 27% reduction in error from previous work. We also show that hybridizing an existing RTE system with our natural logic system yields significant gains on the RTE3 test suite. (shrink)

This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.

There has been a recent surge of work on deontic modality within philosophy of language. This work has put the deontic logic tradition in contact with natural language semantics, resulting in significant increase in sophistication on both ends. This chapter surveys the main motivations, achievements, and prospects of this work.