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  1. Proceeding in Abstraction. From Concepts to Types and the Recent Perspective on Information.Giuseppe Primiero - 2009 - History and Philosophy of Logic 30 (3):257-282.
    This article presents an historical and conceptual overview on different approaches to logical abstraction. Two main trends concerning abstraction in the history of logic are highlighted, starting from the logical notions of concept and function. This analysis strictly relates to the philosophical discussion on the nature of abstract objects. I develop this issue further with respect to the procedure of abstraction involved by (typed) λ-systems, focusing on the crucial change about meaning and predicability. In particular, the analysis of the nature (...)
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  • Alonzo Church:His Life, His Work and Some of His Miracles.Maía Manzano - 1997 - History and Philosophy of Logic 18 (4):211-232.
    This paper is dedicated to Alonzo Church, who died in August 1995 after a long life devoted to logic. To Church we owe lambda calculus, the thesis bearing his name and the solution to the Entscheidungsproblem.His well-known book Introduction to Mathematical LogicI, defined the subject matter of mathematical logic, the approach to be taken and the basic topics addressed. Church was the creator of the Journal of Symbolic Logicthe best-known journal of the area, which he edited for several decades This (...)
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  • Cumulative Habilitation Script.Christoph Benzmüller - 2006 - Saarland University, Germany.
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  • How Fine-Grained is Reality?Peter Fritz - 2017 - Filosofisk Supplement 13 (2):52-57.
  • Type-Logical Semantics.Reinhard Muskens - 2011 - Routledge Encyclopedia of Philosophy Online.
    Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical forms (...)
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  • Arithmetic is Determinate.Zachary Goodsell - forthcoming - Journal of Philosophical Logic:1-24.
    Orthodoxy holds that there is a determinate fact of the matter about every arithmetical claim. Little argument has been supplied in favour of orthodoxy, and work of Field, Warren and Waxman, and others suggests that the presumption in its favour is unjustified. This paper supports orthodoxy by establishing the determinacy of arithmetic in a well-motivated modal plural logic. Recasting this result in higher-order logic reveals that even the nominalist who thinks that there are only finitely many things should think that (...)
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  • Choice and Descriptions in Enriched Intensional Languages — I.R. Routley, R. K. Meyer & L. Goddard - 1974 - Journal of Philosophical Logic 3 (3):291 - 316.
  • The Limits of Computation.Andrew Powell - forthcoming - Axiomathes:1-21.
    This article provides a survey of key papers that characterise computable functions, but also provides some novel insights as follows. It is argued that the power of algorithms is at least as strong as functions that can be proved to be totally computable in type-theoretic translations of subsystems of second-order Zermelo Fraenkel set theory. Moreover, it is claimed that typed systems of the lambda calculus give rise naturally to a functional interpretation of rich systems of types and to a hierarchy (...)
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  • Looking Backwards in Type Logic.Jan Köpping & Thomas Ede Zimmermann - 2021 - Inquiry: An Interdisciplinary Journal of Philosophy 64 (5-6):646-672.
    ABSTRACT Backwards-looking operators Saarinen, E. [1979. “Backwards-Looking Operators in Tense Logic and in Natural Language.” In Essays on Mathematical and Philosophical Logic, edited by J. Hintikka, I. Niiniluoto, and E. Saarinen, 341–367. Dordrecht: Reidel] that have the material in their scope depend on higher intensional operators, are known to increase the expressivity of some intensional languages and have thus played a central role in debates about approaches to intensionality in terms of implicit parameters vs. variables explicitly quantifying over them. The (...)
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  • Intertheoretic Reduction, Confirmation, and Montague’s Syntax-Semantics Relation.Kristina Liefke & Stephan Hartmann - 2018 - Journal of Logic, Language and Information 27 (4):313-341.
    Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. This paper presents a case study of a new type of intertheoretic relation that is inspired by Montague’s analysis of the linguistic syntax-semantics relation. The paper develops a simple model of this relation. To motivate the adoption of our new model, we show that this model (...)
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  • Foundations of applied mathematics I.Jeffrey Ketland - forthcoming - Synthese:1-43.
    This paper aims to study the foundations of applied mathematics, using a formalized base theory for applied mathematics: \ with atoms, where the subscript used refers to a signature specific to the application. Examples are given, illustrating the following five features of applied mathematics: comprehension principles, application conditionals, representation hypotheses, transfer principles and abstract equivalents.
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  • Universal Semantics?Richard Routley - 1975 - Journal of Philosophical Logic 4 (3):327 - 356.
  • Methodology in the Ontology of Artworks: Exploring Hermeneutic Fictionalism.Elisa Caldarola - 2020 - In Concha Martinez Vidal & José Luis Falguera Lopez (ed.), Abstract Objects: For and Against.
    There is growing debate about what is the correct methodology for research in the ontology of artworks. In the first part of this essay, I introduce my view: I argue that semantic descriptivism is a semantic approach that has an impact on meta-ontological views and can be linked with a hermeneutic fictionalist proposal on the meta-ontology of artworks such as works of music. In the second part, I offer a synthetic presentation of the four main positive meta-ontological views that have (...)
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  • Sense and the Computation of Reference.Reinhard Muskens - 2004 - Linguistics and Philosophy 28 (4):473 - 504.
    The paper shows how ideas that explain the sense of an expression as a method or algorithm for finding its reference, preshadowed in Frege’s dictum that sense is the way in which a referent is given, can be formalized on the basis of the ideas in Thomason (1980). To this end, the function that sends propositions to truth values or sets of possible worlds in Thomason (1980) must be replaced by a relation and the meaning postulates governing the behaviour of (...)
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  • A Partial Account of Presupposition Projection.David Beaver & Emiel Krahmer - 2001 - Journal of Logic, Language and Information 10 (2):147-182.
    In this paper it is shown how a partial semantics for presuppositions can be given which is empirically more satisfactory than its predecessors, and how this semantics can be integrated with a technically sound, compositional grammar in the Montagovian fashion. Additionally, it is argued that the classical objection to partial accounts of presupposition projection, namely that they lack “flexibility,” is based on a misconception. Partial logics can give rise to flexible predictions without postulating any ad hoc ambiguities. Finally, it is (...)
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  • The Paradoxes and Russell’s Theory of Incomplete Symbols.Kevin C. Klement - 2014 - Philosophical Studies 169 (2):183-207.
    Russell claims in his autobiography and elsewhere that he discovered his 1905 theory of descriptions while attempting to solve the logical and semantic paradoxes plaguing his work on the foundations of mathematics. In this paper, I hope to make the connection between his work on the paradoxes and the theory of descriptions and his theory of incomplete symbols generally clearer. In particular, I argue that the theory of descriptions arose from the realization that not only can a class not be (...)
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  • Don't Ask, Look! Linguistic Corpora as a Tool for Conceptual Analysis.Roland Bluhm - 2013 - In Migue Hoeltje, Thomas Spitzley & Wolfgang Spohn (eds.), Was dürfen wir glauben? Was sollen wir tun? Sektionsbeiträge des achten internationalen Kongresses der Gesellschaft für Analytische Philosophie e.V. DuEPublico. pp. 7-15.
    Ordinary Language Philosophy has largely fallen out of favour, and with it the belief in the primary importance of analyses of ordinary language for philosophical purposes. Still, in their various endeavours, philosophers not only from analytic but also from other backgrounds refer to the use and meaning of terms of interest in ordinary parlance. In doing so, they most commonly appeal to their own linguistic intuitions. Often, the appeal to individual intuitions is supplemented by reference to dictionaries. In recent times, (...)
     
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  • Making Logical Form Type-Logical: Glue Semantics for Minimalist Syntax.Matthew Gotham - 2018 - Linguistics and Philosophy 41 (5):511-556.
    Glue semantics is a theory of the syntax–semantics interface according to which the syntactic structure of a sentence produces premises in a fragment of linear logic, and the semantic interpretation of the sentence correspond to the proof derivable from those premises. This paper describes how Glue can be connected to a Minimalist syntactic theory and compares the result with the more mainstream approach to the syntax–semantics interface in Minimalism, according to which the input to semantic interpretation is a syntactic structure (...)
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  • The Cooper Storage Idiom.Gregory M. Kobele - 2018 - Journal of Logic, Language and Information 27 (2):95-131.
    Cooper storage is a widespread technique for associating sentences with their meanings, used in diverse linguistic and computational linguistic traditions. This paper encodes the data structures and operations of cooper storage in the simply typed linear \-calculus, revealing the rich categorical structure of a graded applicative functor. In the case of finite cooper storage, which corresponds to ideas in current transformational approaches to syntax, the semantic interpretation function can be given as a linear homomorphism acting on a regular set of (...)
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  • Adjectival and Adverbial Modification: The View From Modern Type Theories.Stergios Chatzikyriakidis & Zhaohui Luo - 2017 - Journal of Logic, Language and Information 26 (1):45-88.
    In this paper we present a study of adjectival/adverbial modification using modern type theories, i.e. type theories within the tradition of Martin-Löf. We present an account of various issues concerning adjectival/adverbial modification and argue that MTTs can be used as an adequate language for interpreting NL semantics. MTTs are not only expressive enough to deal with a range of modification phenomena, but are furthermore well-suited to perform reasoning tasks that can be easily implemented given their proof-theoretic nature. In MTT-semantics, common (...)
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  • Variants of Gödel’s Ontological Proof in a Natural Deduction Calculus.B. Woltzenlogel Paleo & Annika Kanckos - 2017 - Studia Logica 105 (3):553-586.
    This paper presents detailed formalizations of ontological arguments in a simple modal natural deduction calculus. The first formal proof closely follows the hints in Scott’s manuscript about Gödel’s argument and fills in the gaps, thus verifying its correctness. The second formal proof improves the first one, by relying on the weaker modal logic KB instead of S5 and by avoiding the equality relation. The second proof is also technically shorter than the first one, because it eliminates unnecessary detours and uses (...)
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  • On the Number of Types.Miloš Kosterec - 2017 - Synthese 194 (12):5005-5021.
    In this paper, I investigate type theories from several perspectives. First, I present and elaborate the philosophical and technical motivations for these theories. I then offer a formal analysis of various TTs, focusing on the cardinality of the set of types contained in each. I argue that these TTs can be divided into four formal categories, which are derived from the cardinality of the set of their basic elementary types and the finiteness of the lengths of their molecular types. The (...)
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  • Cut-Elimination for Quantified Conditional Logic.Christoph Benzmüller - 2017 - Journal of Philosophical Logic 46 (3):333-353.
    A semantic embedding of quantified conditional logic in classical higher-order logic is utilized for reducing cut-elimination in the former logic to existing results for the latter logic. The presented embedding approach is adaptable to a wide range of other logics, for many of which cut-elimination is still open. However, special attention has to be payed to cut-simulation, which may render cut-elimination as a pointless criterion.
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  • Comparing Approaches To Resolution Based Higher-Order Theorem Proving.Christoph Benzmüller - 2002 - Synthese 133 (1):203-335.
    We investigate several approaches to resolution based automated theoremproving in classical higher-order logic (based on Church's simply typed-calculus) and discuss their requirements with respect to Henkincompleteness and full extensionality. In particular we focus on Andrews'higher-order resolution (Andrews 1971), Huet's constrained resolution (Huet1972), higher-order E-resolution, and extensional higher-order resolution(Benzmüller and Kohlhase 1997). With the help of examples we illustratethe parallels and differences of the extensionality treatment of these approachesand demonstrate that extensional higher-order resolution is the sole approach thatcan completely avoid additional (...)
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  • Formal Semantics: Origins, Issues, Early Impact.Barbara H. Partee - 2011 - The Baltic International Yearbook of Cognition, Logic and Communication 6:13.
    Formal semantics and pragmatics as they have developed since the late 1960's have been shaped by fruitful interdisciplinary collaboration among linguists, philosophers, and logicians, among others, and in turn have had noticeable effects on developments in syntax, philosophy of language, computational linguistics, and cognitive science.In this paper I describe the environment in which formal semantics was born and took root, highlighting the differences in ways of thinking about natural language semantics in linguistics and in philosophy and logic. With Montague as (...)
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  • Grammar Induction by Unification of Type-Logical Lexicons.Sean A. Fulop - 2010 - Journal of Logic, Language and Information 19 (3):353-381.
    A method is described for inducing a type-logical grammar from a sample of bare sentence trees which are annotated by lambda terms, called term-labelled trees . Any type logic from a permitted class of multimodal logics may be specified for use with the procedure, which induces the lexicon of the grammar including the grammatical categories. A first stage of semantic bootstrapping is performed, which induces a general form lexicon from the sample of term-labelled trees using Fulop’s (J Log Lang Inf (...)
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  • Semantic Bootstrapping of Type-Logical Grammar.Sean A. Fulop - 2004 - Journal of Logic, Language and Information 14 (1):49-86.
    A two-stage procedure is described which induces type-logical grammar lexicons from sentences annotated with skeletal terms of the simply typed lambda calculus. First, a generalized formulae-as-types correspondence is exploited to obtain all the type-logical proofs of the sample sentences from their lambda terms. The resulting lexicons are then optimally unified. The first stage constitutes the semantic bootstrapping (Pinker, Language Learnability and Language Development, Harvard University Press, 1984), while the unification procedure of Buszkowski and Penn represents a first attempt at structure-dependent (...)
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  • A Higher-Order Theory of Presupposition.Scott Martin & Carl Pollard - 2012 - Studia Logica 100 (4):727-751.
    So-called 'dynamic' semantic theories such as Kamp's discourse representation theory and Heim's file change semantics account for such phenomena as cross-sentential anaphora, donkey anaphora, and the novelty condition on indefinites, but compare unfavorably with Montague semantics in some important respects (clarity and simplicity of mathematical foundations, compositionality, handling of quantification and coordination). Preliminary efforts have been made by Muskens and by de Groote to revise and extend Montague semantics to cover dynamic phenomena. We present a new higher-order theory of discourse (...)
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  • Natural Language Inference in Coq.Stergios Chatzikyriakidis & Zhaohui Luo - 2014 - Journal of Logic, Language and Information 23 (4):441-480.
    In this paper we propose a way to deal with natural language inference by implementing Modern Type Theoretical Semantics in the proof assistant Coq. The paper is a first attempt to deal with NLI and natural language reasoning in general by using the proof assistant technology. Valid NLIs are treated as theorems and as such the adequacy of our account is tested by trying to prove them. We use Luo’s Modern Type Theory with coercive subtyping as the formal language into (...)
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  • Reasoning About Partial Functions with the Aid of a Computer.William M. Farmer - 1995 - Erkenntnis 43 (3):279 - 294.
    Partial functions are ubiquitous in both mathematics and computer science. Therefore, it is imperative that the underlying logical formalism for a general-purpose mechanized mathematics system provide strong support for reasoning about partial functions. Unfortunately, the common logical formalisms — first-order logic, type theory, and set theory — are usually only adequate for reasoning about partial functionsin theory. However, the approach to partial functions traditionally employed by mathematicians is quite adequatein practice. This paper shows how the traditional approach to partial functions (...)
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  • Completeness in Hybrid Type Theory.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2013 - Journal of Philosophical Logic (2-3):1-30.
    We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret [email protected]_i$ in propositional and first-order hybrid logic. This means: interpret [email protected]_i\alpha _a$ , where $\alpha _a$ is an expression of any type $a$ , as an expression of type $a$ that (...)
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  • Forcing, Downward Löwenheim-Skolem and Omitting Types Theorems, Institutionally.Daniel Găină - 2014 - Logica Universalis 8 (3-4):469-498.
    In the context of proliferation of many logical systems in the area of mathematical logic and computer science, we present a generalization of forcing in institution-independent model theory which is used to prove two abstract results: Downward Löwenheim-Skolem Theorem and Omitting Types Theorem . We instantiate these general results to many first-order logics, which are, roughly speaking, logics whose sentences can be constructed from atomic formulas by means of Boolean connectives and classical first-order quantifiers. These include first-order logic , logic (...)
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  • Recent Developments in Computing and Philosophy.Anthony F. Beavers - 2011 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 42 (2):385-397.
    Because the label "computing and philosophy" can seem like an ad hoc attempt to tie computing to philosophy, it is important to explain why it is not, what it studies (or does) and how it differs from research in, say, "computing and history," or "computing and biology". The American Association for History and Computing is "dedicated to the reasonable and productive marriage of history and computer technology for teaching, researching and representing history through scholarship and public history" (http://theaahc.org). More pervasive, (...)
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  • The Difficulty with the Well-Formedness of Ontological Statements.Guido Küng - 1983 - Topoi 2 (1):111-119.
    When Russell argued for his ontological convictions, for instance that there are negative facts or that there are universals, he expressed himself in English. But Wittgenstein must have noticed that from the point of view of Russell's ideal language these ontological statements appear to be pseudo-propositions. He believed therefore that what these statements pretend to say, could not really be said but only shown. Carnap discovered a way out of this mutism: what in the material mode of speech of the (...)
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  • Adverbs and Events.M. J. Cresswell - 1974 - Synthese 28 (3-4):455 - 481.
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  • A Modern Elaboration of the Ramified Theory of Types.Twan Laan & Rob Nederpelt - 1996 - Studia Logica 57 (2-3):243 - 278.
    The paper first formalizes the ramified type theory as (informally) described in the Principia Mathematica [32]. This formalization is close to the ideas of the Principia, but also meets contemporary requirements on formality and accuracy, and therefore is a new supply to the known literature on the Principia (like [25], [19], [6] and [7]).As an alternative, notions from the ramified type theory are expressed in a lambda calculus style. This situates the type system of Russell and Whitehead in a modern (...)
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  • Formal Semantics in Modern Type Theories with Coercive Subtyping.Zhaohui Luo - 2012 - Linguistics and Philosophy 35 (6):491-513.
    In the formal semantics based on modern type theories, common nouns are interpreted as types, rather than as predicates of entities as in Montague’s semantics. This brings about important advantages in linguistic interpretations but also leads to a limitation of expressive power because there are fewer operations on types as compared with those on predicates. The theory of coercive subtyping adequately extends the modern type theories and, as shown in this paper, plays a very useful role in making type theories (...)
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  • A Note on the Use of Lamda Conversion in Generalized Phrase Structure Grammars.Elisabet Engdahl - 1980 - Linguistics and Philosophy 4 (4):505 - 515.
    The restrictive grammatical format suggested in GPSG provides an extremely interesting alternative to transformational approaches to grammar. However, we have seen that the way the grammar is currently organized, it will in certain cases fail to give the correct interpretation to sentences with displaced constituents. Whenever a left or rightward displaced constituent contains an element that can stand in an anaphoric relation with some other element in the sentence, i.e. contains a quantifier or a pronoun, the semantic rules as given (...)
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  • Combining Montague Semantics and Discourse Representation.Reinhard Muskens - 1996 - Linguistics and Philosophy 19 (2):143 - 186.
    This paper embeds the core part of Discourse Representation Theory in the classical theory of types plus a few simple axioms that allow the theory to express key facts about variables and assignments on the object level of the logic. It is shown how the embedding can be used to combine core analyses of natural language phenomena in Discourse Representation Theory with analyses that can be obtained in Montague Semantics.
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  • A Relational Formulation of the Theory of Types.Reinhard Muskens - 1989 - Linguistics and Philosophy 12 (3):325 - 346.
    This paper developes a relational---as opposed to a functional---theory of types. The theory is based on Hilbert and Bernays' eta operator plus the identity symbol, from which Church's lambda and the other usual operators are then defined. The logic is intended for use in the semantics of natural language.
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  • Carnap’s Defense of Impredicative Definitions.Vera Flocke - 2019 - Review of Symbolic Logic 12 (2):372-404.
    A definition of a property P is impredicative if it quantifies over a domain to which P belongs. Due to influential arguments by Ramsey and Gödel, impredicative mathematics is often thought to possess special metaphysical commitments. It seems that an impredicative definition of a property P does not have the intended meaning unless P already exists, suggesting that the existence of P cannot depend on its explicit definition. Carnap (1937 [1934], p. 164) argues, however, that accepting impredicative definitions amounts to (...)
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  • Reciprocal Influences Between Proof Theory and Logic Programming.Dale Miller - 2021 - Philosophy and Technology 34 (1):75-104.
    The topics of structural proof theory and logic programming have influenced each other for more than three decades. Proof theory has contributed the notion of sequent calculus, linear logic, and higher-order quantification. Logic programming has introduced new normal forms of proofs and forced the examination of logic-based approaches to the treatment of bindings. As a result, proof theory has responded by developing an approach to proof search based on focused proof systems in which introduction rules are organized into two alternating (...)
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  • Traditional Logic and Computational Thinking.J. -Martín Castro-Manzano - 2021 - Philosophies 6 (12):12.
    In this contribution, we try to show that traditional Aristotelian logic can be useful for computational thinking. To achieve this objective, we argue in favor of two statements: that traditional logic is not classical and that logic programming emanating from traditional logic is not classical logic programming.
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  • Why Ramify?Harold T. Hodes - 2015 - Notre Dame Journal of Formal Logic 56 (2):379-415.
    This paper considers two reasons that might support Russell’s choice of a ramified-type theory over a simple-type theory. The first reason is the existence of purported paradoxes that can be formulated in any simple-type language, including an argument that Russell considered in 1903. These arguments depend on certain converse-compositional principles. When we take account of Russell’s doctrine that a propositional function is not a constituent of its values, these principles turn out to be too implausible to make these arguments troubling. (...)
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  • A Simple Proof That Super-Consistency Implies Cut Elimination.Gilles Dowek & Olivier Hermant - 2012 - Notre Dame Journal of Formal Logic 53 (4):439-456.
    We give a simple and direct proof that super-consistency implies the cut-elimination property in deduction modulo. This proof can be seen as a simplification of the proof that super-consistency implies proof normalization. It also takes ideas from the semantic proofs of cut elimination that proceed by proving the completeness of the cut-free calculus. As an application, we compare our work with the cut-elimination theorems in higher-order logic that involve V-complexes.
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  • Semantics with Dependent Types for Indefinites.Justyna Grudzińska - 2016 - Studies in Logic, Grammar and Rhetoric 46 (1):173-192.
    The paper proposes a new semantics with dependent types for indefinites, encompassing both the data related to their exceptional scopal behavior and the data related to their anaphoric properties. The proposal builds on the formal system combining generalized quantifiers with dependent types in [Grudzińska & Zawadowski 2014] and [Grudzińska & Zawadowski 2016].
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  • Linguistic Complexity and Argumentative Unity: A Lvov-Warsaw School Supplement.Peter Simons - 2014 - Studies in Logic, Grammar and Rhetoric 36 (1):101-119.
    It is argued that the source of complexity in language is twofold: repetition, and syntactic embedding. The former enables us to return again and again to the same subject across many sentences, and to maintain the coherence of an argument. The latter is governed by two forms of complexification: the functor-argument structure of all languages and the operator-bound-variable mechanism of familiar formal languages. The former is most transparently represented by categorial grammar, and an extension of this can adequately describe the (...)
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  • Philosophy of Mathematics and Computer Science.Kazimierz Trzęsicki - 2010 - Studies in Logic, Grammar and Rhetoric 22 (35).
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  • Impredicativity and Paradox.Gabriel Uzquiano - 2019 - Thought: A Journal of Philosophy 8 (3):209-221.
    Thought: A Journal of Philosophy, EarlyView.
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  • On the Computational Realization of Formal Ontologies: Formalizing an Ontology of Instantiation in Spacetime Using Isabelle/HOL as a Case Study.Thomas Bittner - 2019 - Applied ontology 14 (3):251-292.
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