Crucial to Peter Achinstein's philosophy of science, as presented in Concepts of Science, is the concept of semantic relevance. First, the concept of semantic relevance is central to his analysis of definition and it is presupposed both in his analysis of the concepts of theory and model and in his critique of alternative analyses. Secondly, Achinstein's way of doing philosophy of science rests heavily on his analysis of semantic relevance. Philosophical analysis for Achinstein seems primarily to consist in specifying the (...) use of certain terms. As we shall see, use and semantic relevance are, according to Achinstein, closely connected.Yet, despite the centrality of this concept in Achinstein's philosophy, I will argue that the concept has serious philosophical problems and that the use Achinstein makes of the concept is dubious. First, I will argue that the notion of semantic relevance inherits some of the traditional problems of analyticity as well as having problems of its own. In particular, I will show that given Achinstein's construal of semantic relevance it is extremely difficult if not impossible to determine the semantic relevance of a term. Secondly, I will maintain that given these problems, Achinstein is not in any way justified in using the notion of semantic relevance in his criticism of other philosophers' views and in the construction of his own. (shrink)

The basic hypothesis of this book is that linguistic reference to kinds should be seen as reference to sortal concepts, i.e. cognitive categories for identifying and classifying objects. Viewed that way, kinds serve as the interface between the conceptual system and the grammatical system. Kind-level predicates differ as to whether they presuppose (e.g. to be extinct) or entail (e.g. to invent) the existence of objects, with crucial consequences for the interpretation of indefinite argument noun phrases. Moreover, object reference always involves (...) underlying kind reference, but kind reference does not always involve object reference. This asymmetry, once recognized, proves useful in solving otherwise puzzling problems in semantic composition. (shrink)

The semilattice relevant logics ∪R, ∪T, ∪RW, and ∪TW are defined by semilattice models in which conjunction and disjunction are interpreted in a natural way. For each of them, there is a cut-free labelled sequent calculus with plural succedents . We prove that these systems are equivalent, with respect to provable formulas, to the restricted systems with single succedents . Moreover, using this equivalence, we give a new Hilbert-style axiomatizations for ∪R and ∪T and prove equivalence between two semantics (...) for the contractionless logics ∪RW and ∪TW. (shrink)

Intentionalism is the view that demonstratives, gradable adjectives, quantifiers, modals and other context‐sensitive expressions are intention‐sensitive: their semantic value on a given use is fixed by speaker intentions. The first aim of this paper is to defend Intentionalism against three recent objections, according to which speakers at least sometimes do not have suitable intentions when using supposedly intention‐sensitive expressions. Its second aim is to thereby shed light on the so far little‐explored question of which kinds of intentions can be (...) class='Hi'>semantically relevant. (shrink)

This paper lays out a program for analysing relevance constructively. It begins with a summary of results concerning the system C of Pottinger [197a] which has entailment, relevant implication, S4 strict implication, and intuitionist implication among its connectives. A full working out of the motivation for C will require formal analysis of informal concepts derived from the usual explanation of the meanings of the constants of intuitionist propositional logic. Formal machinery which should be adequate for the proof theoretic side (...) of the analysis of the nonmodal part of C is described in detail, and the direction in which semantical results are to be sought is indicated. (shrink)

This book is a collection of contributions honouring Arnon Avron’s seminal work on the semantics and proof theory of non-classical logics. It includes presentations of advanced work by some of the most esteemed scholars working on semantic and proof-theoretical aspects of computer science logic. Topics in this book include frameworks for paraconsistent reasoning, foundations of relevance logics, analysis and characterizations of modal logics and fuzzy logics, hypersequent calculi and their properties, non-deterministic semantics, algebraic structures for many-valued logics, and representations of (...) the mechanization of mathematics. Avron’s foundational and pioneering contributions have been widely acknowledged and adopted by the scientific community. His research interests are very broad, spanning over proof theory, automated reasoning, non-classical logics, foundations of mathematics, and applications of logic in computer science and artificial intelligence. This is clearly reflected by the diversity of topics discussed in the chapters included in this book, all of which directly relate to Avron’s past and present works. This book is of interest to computer scientists and scholars of formal logic. (shrink)

Especially in functional-typological linguistics, semantic roles have been studied thoroughly, because they constitute a good starting point for any study on argument marking due to their semantically defined nature. However, the very concept of semantic roles is far from being without problems, and there is still no consensus on how the roles are best defined. In this volume, the notion will be discussed from novel perspectives with the aim of providing new insights into our understanding of semantic roles. Two (...) of the papers deal with semantic role clusters, one with semantic roles in verbless constructions, one with diachrony of semantic roles and two with individual semantic roles that have not been studied in too much detail in previous studies. The book may not offer answers to all questions the readers may have, but at least it raises interesting further questions relevant to arriving at a better understanding of semantic roles. Originally published in Studies in Language Vol. 38:3 (2014). (shrink)

I develop and defend a truthmaker semantics for the relevant logic R. The approach begins with a simple philosophical idea and develops it in various directions, so as to build a technically adequate relevant semantics. The central philosophical idea is that truths are true in virtue of specific states. Developing the idea formally results in a semantics on which truthmakers are relevant to what they make true. A very natural notion of conditionality is added, giving us (...) class='Hi'>relevant implication. I then investigate ways to add conjunction, disjunction, and negation; and I discuss how to justify contraposition and excluded middle within a truthmaker semantics. (shrink)

My immediate conclusion, therefore, is a modest one. I only specifically rule out the semantic convention for definite descriptions in which the semantic referent just is the speaker's referent. In arguing for that I carefully avoided relying on the helpfulness assumption. But I did, implicitly, make use of the following procedure.In examining a claim that C is the semantic convention (or form of convention) for a term (or class of term), check to see that C is capable of being helpful (...) to the extent that an inspection of cases of successful communication employing that term shows it must be.My broader moral is that such a procedure should be employed in determining what are our semantic conventions. (shrink)

Possible-world semantics are provided for Parikh’s relevance-sensitive model for belief revision. Having Grove’s system-of-spheres construction as a base, we consider additional constraints on measuring distance between possible worlds, and we prove that, in the presence of the AGM postulates, these constraints characterize precisely Parikh’s axiom (P). These additional constraints essentially generalize a criterion of similarity that predates axiom (P) and was originally introduced in the context of Reasoning about Action. A by-product of our study is the identification of two possible (...) readings of Parikh’s axiom (P), which we call the strong and the weak versions of the axiom. An interesting feature of the strong version is that, unlike classical AGM belief revision, it makes associations between the revision policies of different theories. (shrink)

In 1988, Kit Fine published a semantic theory for quantified relevant logics. He referred to this theory as stratified semantics. While it has received some attention in the literature, 1–20, 1992; Mares & Goldblatt, Journal of Symbolic Logic 71, 163–187, 2006), stratified semantics has overall received much less attention than it deserves. There are two plausible reasons for this. First, the only two dedicated treatments of stratified semantics available are, 27–59, 1988; Mares, Studia Logica 51, 1–20, 1992), both of (...) which are quite dense and technically challenging. Second, there are a number of prima facie reasons to be worried about stratified semantics. The purpose of this paper is to revitalize research on stratified semantics. I will do so by giving a ‘user friendly’ presentation of the semantics, and by giving reasons to think that the prima facie reasons to be worried about it are too simplistic. (shrink)

This book explores some of Kit Fine's outstanding contributions to logic, philosophy of language, philosophy of mathematics, and metaphysics, among others. Contributing authors address in-depth issues about truthmaker semantics, counterfactual conditionals, grounding, vagueness, non-classical consequence relations, and arbitrary objects, offering critical reflections and novel research contributions. Each chapter is accompanied by an extensive commentary, in which Kit Fine offers detailed responses to the ideas and themes raised by the contributors. The book includes a brief autobiography and exhaustive list of his (...) publications to this date. This book is of interest to logicians of all stripes and to analytic philosophers more generally. (shrink)

The past decade has witnessed the emergence of a novel stance on semantic representation, and its relationship to context sensitivity. Connectionist-minded philosophers, including Clark and van Gelder, have espoused the merits of viewing hidden-layer, context-sensitive representations as possessing semantic content, where this content is partially revealed via the representations'' position in vector space. In recent work, Bodén and Niklasson have incorporated a variant of this view of semantics within their conception of semantic systematicity. Moreover, Bodén and Niklasson contend that they (...) have produced experimental results which not only satisfy a kind of context-based, semantic systematicity, but which, to the degree that reality permits, effectively deals with challenges posed by Fodor and Pylyshyn (1988), and Hadley (1994a). The latter challenge involved well-defined criteria for strong semantic systematicity. This paper examines the relevant claims and experiments of Bodén and Niklasson. It is argued that their case fatally involves two fallacies of equivocation; one concerning ''semantic content'' and the other concerning ''novel test sentences''. In addition, it is argued that their ultimate construal of context sensitive semantics contains serious confusions. These confusions are also found in certain publications dealing with "latent semantic analysis". Thus, criticisms presented here have relevance beyond the work of Bodén and Niklasson. (shrink)

This paper continues the work of Priest and Sylvan in Simplified Semantics for Basic Relevant Logics, a paper on the simplified semantics of relevant logics, such as B⁺ and B. We show that the simplified semantics can also be used for a large number of extensions of the positive base logic B⁺, and then add the dualising '*' operator to model negation. This semantics is then used to give conservative extension results for Boolean negation.

Recently several papers have reported relevance effects on the cognitive assessments of indicative conditionals, which pose an explanatory challenge to the Suppositional Theory of conditionals advanced by David Over, which is influential in the psychology of reasoning. Some of these results concern the “Equation” (P(if A, then C) = P(C|A)), others the de Finetti truth table, and yet others the uncertain and-to-inference task. The purpose of this chapter is to take a Birdseye view on the debate and investigate some of (...) the open theoretical issues posed by the empirical results. Central among these is whether to count these effects as belonging to pragmatics or semantics. (shrink)

In his original semantics for counterfactuals, David Lewis presupposed that the ordering of worlds relevant to the evaluation of a counterfactual admitted no incomparability between worlds. He later came to abandon this assumption. But the approach to incomparability he endorsed makes counterintuitive predictions about a class of examples circumscribed in this paper. The same underlying problem is present in the theories of modals and conditionals developed by Bas van Fraassen, Frank Veltman, and Angelika Kratzer. I show how to reformulate (...) all these theories in terms of lower bounds on partial preorders, conceived of as maximal antichains, and I show that treating lower bounds as cutsets does strictly better at capturing our intuitions about the semantics of modals, counterfactuals, and deontic conditionals. (shrink)

As introduction to the special issue on the semantics of cardinals, we offer some background on the relevant literature, and an overview of the contributions to this volume. Most of these papers were presented in earlier form at an interdisciplinary workshop on the topic at The Ohio State University, and the contributions to this issue reflect that interdisciplinary character: the authors represent both fields in the title of this journal.

This paper develops a semantic account of morphological number marking, specifically in the presence of numerals. In addition to accounting for number marking on basic nouns like _book_ in English, the account handles variation in patterns of number marking along two dimensions: cross-linguistically, between languages that either necessitate or prohibit singular morphology in the presence of numerals greater than ‘one’; and within one and the same language on the various nominal elements in English. Building off the presuppositional approach to morphological (...) number from Sauerland (Proc SALT 13:258–275, 2003), the proposed semantics accounts for both sorts of variation by assuming flexibility in the selection of the measure relevant to the one-ness presupposition of the morphological singular form. (shrink)

Werkmeister's new book, The Basis and Structure of Knowledge is the second major attempt in recent years to defend the idealistic theory of knowledge. The first was Blanshard's Nature of Thought; and it is worth noticing that both authors, in undertaking the defense of a position long in the shadows, are well aware of contemporary developments in logic and technical philosophy. Werkmeister freely acknowledges his debt to Blanshard; yet his work differs in scope from the latter's in at least two (...) ways. Firstly, the more recent book is concerned largely with the epistemological analysis of meaning and truth and hardly at all with what an older generation called "philosophical psychology," while philosophical psychology fills all of the first and part of the second volume of Blanshard's work. In my opinion, this is all to the good. (That our generation inverts the error and too often indulges in psychological philosophy is another story!) Secondly, Werkmeister presents us with detailed analyses of scientific method, of the structure of scientific theories, and of mathematics, all three areas to which Blanshard pays virtually no attention. The First Part of Werkmeister's book treats of Language and Meaning; the Second of Truth and the World About Us, the Third of Formal Knowledge, and the Fourth Part deals with Empirical Knowledge. But there is a fundamental thesis that runs through all of this. The analysis of each of these four domains reveals, according to Werkmeister, that only a coherence theory of meaning and truth can adequately reflect the criteria actually used by science and commonsense. It is not my intention to rehearse here the familiar dialectic of the arguments for and against this doctrine; the less so, since Werkmeister himself gives a useful review of both sides of the controversy. Rather, I want to try to fix as precisely as possible, within the context of Werkmeister's discussion, the nature of the difference between coherence theories on the one hand and correspondence theories on the other. This difference has not always been too clearly stated; it even seems that recent developments in linguistic analysis have been the occasion for some new confusions on this very point. For coherence theorists who have recognized that philosophical semantics is a "formal" discipline now insist that "to say what a symbol means is not to relate it to an object, but to give it an interpretation in terms of other symbols," as Ayer2 has recently put it. This seems to contradict the "comparison with fact" feature of the traditional realistic formulations of the correspondence view. A superficial bystander could even believe that the correspondence theorists have given up their original position, since both sides now agree that truth is a matter of a relation between symbols. Such agreement, as I hope to show, is more apparent than real, for what is now at stake is the nature of that "intrasymbolic relation." And on this nature the two parties disagree. There is little doubt that Werkmeister's book appears at a moment more propitious for the advocacy of the coherence theory of truth than did Blanshard's. In the near decade that separates the two works the intellectual climate has become, for better or for worse, considerably more favorable to a reconsideration of, and possibly even a reconciliation with, some of the major tenets of rationalism. This is reflected in the current discussion regarding the contrary-to-fact conditional, the dissatisfaction with material implication, and the correlative concern for a more adequate analysis of the concept of a natural law. It is evident too in the revived enthusiasm for intensional logic and in the related interest in the modalities. As uncompromising an empiricist as C. L. Lewis, with whom, by the way, Werkmeister shares a common Kantian background, has introduced into his latest work a "congruence" theory of truth which, despite the substitution of a so-called "probability" inference for necessary inference, looks very much like the coherance criterion all over again. So Werkmeister's book should be welcome for its clear presentation of the relevant issues; and even those who disagree with him can admire the candor and forthrightness with which he champions what remains, despite vacillations, an essentially unpopular position. (shrink)

This note explains an error in Restall’s ‘Simplified Semantics for Relevant Logics (and some of their rivals)’ (Restall, J Philos Logic 22(5):481–511, 1993 ) concerning the modelling conditions for the axioms of assertion A → (( A → B ) → B ) (there called c 6) and permutation ( A → ( B → C )) → ( B → ( A → C )) (there called c 7). We show that the modelling conditions for assertion and permutation (...) proposed in ‘Simplified Semantics’ overgenerate. In fact, they overgenerate so badly that the proposed semantics for the relevant logic R validate the rule of disjunctive syllogism. The semantics provides for no models of R in which the “base point” is inconsistent. This problem is not restricted to ‘Simplified Semantics.’ The techniques of that paper are used in Graham Priest’s textbook An Introduction to Non-Classical Logic (Priest, 2001 ), which is in wide circulation: it is important to find a solution. In this article, we explain this result, diagnose the mistake in ‘Simplified Semantics’ and propose two different corrections. (shrink)

The Routley-Meyer relational semantics for relevant logics is extended to give a sound and complete model theory for many propositionally quantified relevant logics (and some non-relevant ones). This involves a restriction on which sets of worlds are admissible as propositions, and an interpretation of propositional quantification that makes ∀ pA true when there is some true admissible proposition that entails all p -instantiations of A . It is also shown that without the admissibility qualification many of the (...) systems considered are semantically incomplete, including all those that are sub-logics of the quantified version of Anderson and Belnap’s system E of entailment, extended by the mingle axiom and the Ackermann constant t . The incompleteness proof involves an algebraic semantics based on atomless complete Boolean algebras. (shrink)

The main idea in this series of essays is that subjective awareness depends upon the intralaminar nuclei of each thalmus. This implies that the internal structure and external relations of ILN make subjective awareness possible. An array of material relevant to this proposal was briefly reviewed in Part I. This Part II considers in more detail some semantic aspects and a bit of philosophic background as these pertain to propositions 0, 1, and 2 of Part I. Part II should (...) be read in conjunction with Part I. (shrink)

Two semantic paradoxes, the Liar and Curry’s paradox, are analysed using a newly developed conception of procedural semantics (semantics according to which the truth of propositions is determined algorithmically), whose main characteristic is its departure from methodological realism. Rather than determining pre-existing facts, procedures are constitutive of them. Of this semantics, two versions are considered: closed (where the halting of procedures is presumed) and open (without this presumption). To this end, a procedural approach to deductive reasoning is developed, based on (...) the idea of simulation. As is shown, closed semantics supports classical logic, but cannot in any straightforward way accommodate the concept of truth. In open semantics, where paradoxical propositions naturally ‘belong’, they cease to be paradoxical; yet, it is concluded that the natural choice—for logicians and common people alike—is to stick to closed semantics, pragmatically circumventing problematic utterances. (shrink)

I outline a truthmaker semantics for relevanced logic.

The last several decades of research on counterfactual conditionals in the fields of philosophy and linguistics have yielded a predominant paradigm according to which the notion of similarity plays the starring role. Roughly, a counterfactual of the form A > C is true iff the closest A-worlds are all C-worlds, where the closeness of a world is a function of its similarity, in a certain sense, to the actual world. I argue that this is deeply misguided. In some cases we (...) may only care about the closest A-worlds, but quite often we care about some broader variety of A-worlds varying in closeness. After presenting several problem cases for the similarity-based paradigm, some new and some known, I propose an alternative paradigm for the semantics of counterfactuals, which introduces the notion of A-scenarios, understood roughly as different ways of making A true. According to this view, A > C is true iff all the contextually relevant ways of making A true also make C true. I then more carefully spell out a working view that formalizes this idea with greater precision, and explore the consequences of that version of the view. (shrink)

The purpose of teaching logic in philosophy is to enable us to evaluate arguments with respect to (formal) validity. Standard logics refer to a concept of validity which allows for the relation of implication to hold between premises and conclusion even in cases where there is no “relevant” connection between the premises and the conclusion. A prominent example for this is the rule “Ex-Falso-Quodlibet” (EFQ), which allows us to infer an arbitrary proposition from a contradiction. The tolerance of irrelevance (...) endorsed by standard logics unfortunately engenders that they cannot adequately fulfill their intended task of analyzing and evaluating philosophical, scientific and everyday-life arguments – instead, their application even gives rise to a multitude of artificial philosophical pseudoproblems (like the problem of the disposition predicates or the problem of counterfactuals). As alternatives to standard logics, there exist non-standard systems called “relevance logics” or “relevant logics” meant to avoid irrelevance. The problem with these systems, however, is that the mainstream relational semantics (“worlds semantics”) available for them is to be considered unintuitive and complex to a degree which is apt to render relevant logics unattractive to the majority of philosophers who are on the lookout not only for adequate, but also simple and efficient technical means for evaluating arguments. Therefore, the main aim of this treatise is to provide an alternative semantics (“rules semantics”) which is comparatively easy to grasp and simple in application. A second aim of the book is to extend the semantics as least as far as it takes to cover more or less all the logical notions philosophers need in their “everyday analyzing”. This includes first order predicate logic, higher order logic (for analyzing talk about “properties” etc.), identity, definite descriptions, abstraction principles and modal logic. This book can be read without having any more background than a good introductory course in classical logic provides. (shrink)

This paper gives an outline of three different approaches to the four-valued semantics for relevant logics (and other non-classical logics in their vicinity). The first approach borrows from the 'Australian Plan' semantics, which uses a unary operator '⋆' for the evaluation of negation. This approach can model anything that the two-valued account can, but at the cost of relying on insights from the Australian Plan. The second approach is natural, well motivated, independent of the Australian Plan, and it provides (...) a semantics for the contraction-free relevant logic C (or RW). Unfortunately, its approach seems to model little else. The third approach seems to capture a wide range of formal systems, but at the time of writing, lacks a completeness proof. (shrink)

This paper proves decidability of a range of weak relevant logics using decision procedures based on the Routley-Meyer semantics. Logics are categorized as F-logics, for those proved decidable using a filtration method, and U-logics, for those proved decidable using a direct (unfiltered) method. Both of these methods are set out as reductio methods, in the style of Hughes and Cresswell. We also examine some extensions of the U-logics where the method fails and infinite sequences of worlds can be generated.

The Semantic-Pragmatic Analysis of Persian Modal Verbs Based on Papafragou's Model This paper aims at analyzing the semantics and pragmatics of Persian modal verbs based on Papafragou's relevance-theoretic model. Persian modals are defined in terms of logical relations and propositional domains. According to the findings of the research, two of the three modals, namely, šodan and tavân express the logical relation of compatibility with respect to different propositional domains: the three forms mišavad, mišod and mišode are unspecified with respect to (...) their propositional domains and take them directly from the context, whereas betavân and bešavad accept the desirability domain. Mitavân also expresses compatibility in relation to the propositions in the factual domain. However, bˇyad is the only modal that encodes the logical relation of entailment and is unspecified with respect to the type of propositional domain it accepts. (shrink)

Grice's distinction between what is said by a sentence and what is implicated by an utterance of it is both extremely familiar and almost universally accepted. However, in recent literature, the precise account he offered of implicature recovery has been questioned and alternative accounts have emerged. In this paper, I examine three such alternative accounts. My main aim is to show that the two most popular accounts in the current literature still face signifi cant problems. I will then conclude by (...) suggesting that an alternative account, emerging from semantic minimalism, is best placed to accommodate Grice's distinction. (shrink)

A natural way of understanding (non-epistemic) looks talk in natural language is phenomenalist: to ascribe looks to objects is to say something about the way they strike us when we look at them. This explains why the truth values of looks-sentences intuitively vary with the circumstances with respect to which they are evaluated. But Mike Martin (2010) argues that there is no semantic reason to prefer a phenomenalist understanding of looks to “Parsimony”, the position according to which looks are basic (...) visible properties. He suggests a semantics for looks-sentences that explains their intuitive truth values and is compatible with Parsimony. I argue that there is semantic reason to prefer a phenomenalist understanding of looks to a parsimonious one since there is a simpler semantics compatible with a phenomenalist understanding of looks, but not with Parsimony. This semantics provides a better explanation of the relevant truth value distribution. (shrink)

Minimal Semantics asks what a theory of literal linguistic meaning is for - if you were to be given a working theory of meaning for a language right now, what would you be able to do with it? Emma Borg sets out to defend a formal approach to semantic theorising from a relatively new type of opponent - advocates of what she call 'dual pragmatics'. According to dual pragmatists, rich pragmatic processes play two distinct roles in linguistic comprehension: as well (...) as operating in a post-semantic capacity to determine the implicatures of an utterance, they also operate prior to the determination of truth-conditional content for a sentence. That is to say, they have an integral role to play within what is usually thought of as the semantic realm. Borg believes dual pragmatic accounts constitute the strongest contemporary challenge to standard formal approaches to semantics since they challenge the formal theorist to show not merely that there is some role for formal processes on route to determination of semantic content, but that such processes are sufficient for determining content. Minimal Semantics provides a detailed examination of this school of thought, introducing readers who are unfamiliar with the topic to key ideas like relevance theory and contextualism, and looking in detail at where these accounts diverge from the formal approach. Borg's defence of formal semantics has two main parts: first, she argues that the formal approach is most naturally compatible with an important and well-grounded psychological theory, namely the Fodorian modular picture of the mind. Then she argues that the main arguments adduced by dual pragmatists against formal semantics - concerning apparent contextual intrusions into semantic content - can in fact be countered by a formal theory. The defence holds, however, only if we are sensitive to the proper conditions of success for a semantic theory. Specifically, we should reject a range of onerous constraints on semantic theorizing (e.g., that it answer epistemic or metaphysical questions, or that it explain our communicative skills) and instead adopt a quite minimal picture of semantics. (shrink)

This paper sets out two semantics for the relevant logic R based on Dunn's four-valued semantics for first-degree entailments. Unlike Routley's semantics for weak relevant logics, they do not use two ternary accessibility relations. Unlike Restall's semantics, they capture all of R. But there is a catch. Both of the present semantics are neighbourhood semantics, that is, they include sets of propositions in the specification of their frames.

Once upon a time, modal logic was castigated because it ‘had no semantics.’ Kripke, Hintikka, Kanger, and others changed all that. In a similar way, when Relevant Logic was introduced by Anderson and Belnap, it too was castigated for ‘having no semantics.’ The present overview marks a culmination of that effort. The semantic approach described here brings together a number of hitherto disparate efforts to set out formal systems for logics of relevant implication and entailment. It also makes (...) clear (despite some of our hopes and utterances) that the One True Logic does not exist. This is as true for relevant logics as Kripke et al., showed it to be for modal logics. In both cases, subtle (and not so subtle) variations on semantical postulates produce different logics in the same family. The question of which semantical postulates are correct makes no sense without further context, i.e., the questioner needs to answer the question: Correct for what? The question that does remain is: What motivates the relevant family of logics? And this is the question that is the main job for this chapter to investigate. (shrink)

We present an algebraic-style of semantics, which we call a content semantics, for quantified relevant logics based on the weak system BBQ. We show soundness and completeness for all quantificational logics extending BBQ and also treat reduced modelling for all systems containing BB d Q. The key idea of content semantics is that true entailments AB are represented under interpretation I as content containments, i.e. I(A)I(B) (or, the content of A contains that of B). This is opposed to the (...) truth-functional way which represents true entailments as truth-preservations over all set-ups (or worlds), i.e. (VaK) (if I(A, a) = T then I(B, a)= T). (shrink)

Modus ponens provides the central theme. There are laws, of the form A→C. A logic L collects such laws. Any datum A provides input to the laws of L. The central ternary relation R relates theories L,T and U, where U consists of all of the outputs C got by applying modus ponens to major premises from L and minor premises from T. Underlying this relation is a modus ponens product operation on theories L and T, whence RLTU iff LTU. (...) These ideas have been expressed, especially with Routley, as worlds semantics for relevant and other substructural logics.Worlds are best demythologized as theories, subject to truth-functional and other constraints. The chief constraint is that theories are taken as closed under logical entailment, which clearly begs the question if we are using the semantics to determine which theory L is Logic itself. Instead we draw the modal logicians’ conclusion—there are many substructural logics, each with its appropriate ternary relational postulates.Each logic L gives rise to a Calculus of L-theories, on which particular candidate logical axioms have the combinatorial properties expected from the well-known Curry–Howard isomorphism . We apply their bubbling lemma, updating the Fools Model of Combinatory Logic at the pure → level for the system BT. We make fusion an explicit connective, proving a combinator correspondence theorem. Having taken relevant → as a left residual for , we explore its right residual mate →r. Finally we concentrate on and prove a finite model property for the classical minimal relevant logic CB, a conservative extension of the minimal positive relevant logic B+. (shrink)

As many philosophers agree, the frame problem is concerned with how an agent may efficiently filter out irrelevant information in the process of problem-solving. Hence, how to solve this problem hinges on how to properly handle semantic relevance in cognitive modeling, which is an area of cognitive science that deals with simulating human's cognitive processes in a computerized model. By "semantic relevance", we mean certain inferential relations among acquired beliefs which may facilitate information retrieval and practical reasoning under certain epistemic (...) constraints, e. g., the insufficiency of knowledge, the limitation of time budget, etc. However, traditional approaches to relevance—as for example, relevance logic, the Bayesian approach, as well as Description Logic—have failed to do justice to the foregoing constraints, and in this sense, they are not proper tools for solving the frame problem/relevance problem. As we will argue in this paper, Non-Axiomatic Reasoning System (NARS) can handle the frame problem in a more proper manner, because the resulting solution seriously takes epistemic constraints on cognition as a fundamental theoretical principle. (shrink)

Feedback such as backchannels and clarification requests often occurs subsententially, demonstrating the incremental nature of grounding in dialogue. However, although such feedback can occur at any point within an utterance, it typically does not do so, tending to occur at Feedback Relevance Spaces. We present a corpus study of acknowledgements and clarification requests in British English, and describe how our low-level, semantic processing model in Dynamic Syntax accounts for this feedback. The model trivially accounts for the 85% of cases where (...) feedback occurs at FRSs, but we also describe how it can be integrated or interpreted at non-FRSs using the predictive, incremental and interactive nature of the formalism. This model shows how feedback serves to continually realign processing contexts and thus manage the characteristic divergence and convergence that is key to moving dialogue forward. (shrink)

One of the hottest philosophical debates in recent years concerns the nature of the semantics/pragmatics divide. Some writers have expressed the reserve that this might be merely terminological, but in my view it ultimately concerns a substantive issue with empirical implications: the scope and limits of a serious scientific undertaking, formal semantics. In this critical note I discuss two arguments by Recanati: his main methodological argument --viz. that the contents posited by what he calls 'literalists' play no relevant role (...) in communication--, and some phenomenological considerations regarding the "Availability Principle" that he appeals to in order to buttress that main argument. /// Uno de los más encarnizados debates filosóficos recientes atañe a la naturaleza de la distinción entre semántica y pragmática. Aunque algunos autores han expresado reservas en el sentido de que èste pudiera ser sólo terminológico, en mi opinión tiene que ver con una cuestión sustantiva con implicaciones empíricas: el alcance y los límites de una empresa científica seria, la semántica formal. En este texto discuto dos argumentos de Recanati: su principal argumento metodológico, que los contenidos postulados por los autores que él denomina "literalistas" no desempeñan ningùn papel relevante en la comunicación, y, en segundo lugar, ciertas consideraciones fenomenológicas en torno a su "Principio de Accesibilidad", a las cuales apela para apoyar el argumento metodológico. (shrink)

This paper defines a Sahlqvist fragment for relevant logic and establishes that each class of frames in the Routley-Meyer semantics which is definable by a Sahlqvist formula is also elementary, that is, it coincides with the class of structures satisfying a given first order property calculable by a Sahlqvist-van Benthem algorithm. Furthermore, we show that some classes of Routley-Meyer frames definable by a relevant formula are not elementary.