Results for 'type logic'

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  1. Categorial Type Logics.Michael Moortgat - 1997 - In J. F. A. K. Van Benthem, Johan van Benthem & Alice G. B. Ter Meulen (eds.), Handbook of Logic and Language. Elsevier.
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  2.  57
    Type Logics and Pregroups.Wojciech Buszkowski - 2007 - Studia Logica 87 (2-3):145-169.
    We discuss the logic of pregroups, introduced by Lambek [34], and its connections with other type logics and formal grammars. The paper contains some new ideas and results: the cut-elimination theorem and a normalization theorem for an extended system of this logic, its P-TIME decidability, its interpretation in L1, and a general construction of (preordered) bilinear algebras and pregroups whose universe is an arbitrary monoid.
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  3.  29
    Type-logical semantics.Bob Carpenter - 1997 - Cambridge: MIT Press.
    The book, which stepwise develops successively more powerful logical and grammatical systems, covers an unusually broad range of material.
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  4. Anaphora and Type Logical Grammar.David Dowty - unknown
    (2) Type Logical Grammar (Moortgat & Oehrle 1994, Morrill 1994. Moortgat 1996): i. Grammar as a deductive system; variant of linear logic; two deductive rules for each type constructor (=; n; ): elimination ( modus ponens) and introduction ( rule of conditional proof).
     
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  5. 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. (...)
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  6.  17
    Typed logics with states.J. van Eijck - 1997 - Logic Journal of the IGPL 5 (5):623-645.
    The paper presents a simple format for typed logics with states by adding a function for register update to standard typed lambda calculus. It is shown that universal validity of equality for this extended language is decidable . This system is next extended to a full fledged typed dynamic logic, and it is illustrated how the resulting format allows for very simple and intuitive representations of dynamic semantics for natural language and denotational semantics for imperative programming. The proposal is (...)
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  7.  19
    Logical Foundations for Hybrid Type-Logical Grammars.Richard Moot & Symon Jory Stevens-Guille - 2022 - Journal of Logic, Language and Information 31 (1):35-76.
    This paper explores proof-theoretic aspects of hybrid type-logical grammars, a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also present both a sequent and a proof net calculus for hybrid type-logical grammars. In addition to clarifying the logical foundations of hybrid type-logical grammars, the current study opens the way to variants and extensions of the original system, including but not limited to (...)
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  8.  87
    Complete infinitary type logics.J. W. Degen - 1999 - Studia Logica 63 (1):85-119.
    For each regular cardinal κ, we set up three systems of infinitary type logic, in which the length of the types and the length of the typed syntactical constructs are $\Sigma _{}$, the global system $\text{g}\Sigma _{}$ and the τ-system $\tau \Sigma _{}$. A full cut elimination theorem is proved for the local systems, and about the τ-systems we prove that they admit cut-free proofs for sequents in the τ-free language common to the local and global systems. These (...)
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  9.  31
    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 (...)
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  10.  28
    Lindenbaum-Type Logical Structures.Sayantan Roy, Sankha S. Basu & Mihir K. Chakraborty - 2023 - Logica Universalis 17 (1):69-102.
    In this paper, we study some classes of logical structures from the universal logic standpoint, viz., those of the Tarski- and the Lindenbaum-types. The characterization theorems for the Tarski- and two of the four different Lindenbaum-type logical structures have been proved as well. The separations between the five classes of logical structures, viz., the four Lindenbaum-types and the Tarski-type have been established via examples. Finally, we study the logical structures that are of both Tarski- and a Lindenbaum- (...), show their separations, and end with characterization, adequacy, minimality, and representation theorems for one of the Tarski–Lindenbaum-type logical structures. (shrink)
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  11.  25
    Resource sharing in type logical grammar.Gerhard Jäger - 2003 - In R. Oehrle & J. Kruijff (eds.), resource sensitivity, binding, and anaphora. kluwer. pp. 97--121.
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  12. Types of negation in logical reconstructions of meinong Andrew Kenneth Jorgensen university of Leeds.in Logical Reconstructions Of Meinong - 2004 - Grazer Philosophische Studien 67 (1):21-36.
     
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  13.  56
    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 (...)
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  14.  6
    A Type-Logic Approach to Refinement.Julia Barragan - 1996 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 11 (2):91-103.
    Beyond any doubt the pragmatical-based improvements introduced in the rules of inference during the process of refinement of a legal expert system may be efficient but they hardly will be capable to provide a point of reference for a more general correctness measure. During the refinement of KBSLEX the debate of the Theory of Legal Argument has contributed to illuminate the point suggesting that the modeling of legal reasoning and legal decision making should be grounded on a logical approach but (...)
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  15.  18
    On bound anaphora in type logical grammar.Glyn Morrill - 2003 - In R. Oehrle & J. Kruijff (eds.), resource sensitivity, binding, and anaphora. kluwer. pp. 159--177.
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  16. (1 other version)First-Order, Curry-Typed Logic for Natural Language Semantics.Chris Fox, Shalom Lappin & Carl Pollard - unknown
    The paper presents Property Theory with Curry Typing where the language of terms and well-formed formulæ are joined by a language of types. In addition to supporting fine-grained intensionality, the basic theory is essentially first-order, so that implementations using the theory can apply standard first-order theorem proving techniques. The paper sketches a system of tableau rules that implement the theory. Some extensions to the type theory are discussed, including type polymorphism, which provides a useful analysis of conjunctive terms. (...)
     
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  17. Bound Anaphora and Type Logical Grammar.David Dowty - unknown
    (Though it is now known that many pronouns once lumped under ”bound variables” are in fact referential indefinites or other phenomena better accounted for in a DRT-like view of referents, there remain many true instances of sentenceinternally bound anaphora: this talk concerns only the latter.) Almost all versions of categorial grammar (CG) are differentiated from other syntactic theories in treating a multi-argument verb as an Ò-place predicate phrase (PrdP) that combines with a NP or other argument to yield a (Ò-1)-place (...)
     
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  18.  47
    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 (...)
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  19. 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 (...)
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  20. Introducing equational type logic.V. Manca, A. Salibra & G. Scollo - 1991 - Journal of Symbolic Logic 56:1132.
     
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  21.  10
    A multimodal type logical grammar analysis of Japanese: word order and quantifier scope.Rui Otake & Kei Yoshimoto - 2008 - In Takashi Washio, Ken Satoh, Hideaki Takeda & Akihiro Inokuchi (eds.), New Frontiers in Artificial Intelligence. Springer. pp. 135--148.
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  22.  64
    Types as graphs: Continuations in type logical grammar. [REVIEW]Chris Barker & Chung-Chieh Shan - 2006 - Journal of Logic, Language and Information 15 (4):331-370.
    Using the programming-language concept of continuations, we propose a new, multimodal analysis of quantification in Type Logical Grammar. Our approach provides a geometric view of in-situ quantification in terms of graphs, and motivates the limited use of empty antecedents in derivations. Just as continuations are the tool of choice for reasoning about evaluation order and side effects in programming languages, our system provides a principled, type-logical way to model evaluation order and side effects in natural language. We illustrate (...)
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  23.  42
    Calculating Zero Pronominals in Situ: A Type Logical Approach.Haixia Man, Chongli Zou & Kesheng Li - 2022 - Complexity 2022:1-8.
    Zero pronominals challenge Type Logical Grammar in two ways. One, TLG displays a linear resource management regime for semantic composition, meaning that pronominals call for special treatment if they want to do resource multiplication. Two, as a grammar of lexicalism, TLG applies to phonologically realized lexical entries only, illegitimating the phonetically null items during syntactic derivation. Jägor extends the inventory of category-forming connectives of TLG by a third kind of implication that creates categories of anaphoric items and solves the (...)
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  24.  39
    Carpenter Bob. Type-logical semantics. Language, speech, and communication series. Bradford books. The MIT Press, Cambridge, Mass., and London, 1997, xxi + 575 pp. [REVIEW]Mati Pentus - 1999 - Journal of Symbolic Logic 64 (4):1835-1836.
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  25. Deductive and Grammatical Competence: Type Logical Remarks on Nesting Phenomena.Daniele Porello - 2007 - Epistemologia 30 (2):281-306.
  26. Type-theoretic logic with an operational account of intensionality.Shalom Lappin & Chris Fox - 2015 - Synthese 192 (3):563-584.
    We formulate a Curry-typed logic with fine-grained intensionality within Turner’s typed predicate logic. This allows for an elegant presentation of a theory that corresponds to Fox and Lappin’s property theory with curry typing, but without the need for a federation of languages. We then consider how the fine-grained intensionality of this theory can be given an operational interpretation. This interpretation suggests itself as expressions in the theory can be viewed as terms in the untyped lambda-calculus, which provides a (...)
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  27.  88
    Epistemic logic meets epistemic game theory: a comparison between multi-agent Kripke models and type spaces.Paolo Galeazzi & Emiliano Lorini - 2016 - Synthese 193 (7):2097-2127.
    In the literature there are at least two main formal structures to deal with situations of interactive epistemology: Kripke models and type spaces. As shown in many papers :149–225, 1999; Battigalli and Siniscalchi in J Econ Theory 106:356–391, 2002; Klein and Pacuit in Stud Log 102:297–319, 2014; Lorini in J Philos Log 42:863–904, 2013), both these frameworks can be used to express epistemic conditions for solution concepts in game theory. The main result of this paper is a formal comparison (...)
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  28.  28
    Logical Forms, Substitutions and Information Types.Vít Punčochář - 2023 - Logic and Logical Philosophy 32 (3):459--473.
    This paper explores the relation between the philosophical idea that logic is a science studying logical forms, and a mathematical feature of logical systems called the principle of uniform substitution, which is often regarded as a technical counterpart of the philosophical idea. We argue that at least in one interesting sense the principle of uniform substitution does not capture adequately the requirement that logic is a matter of form and that logical truths are formal truths. We show that (...)
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  29.  51
    Modal‐type orthomodular logic.Graciela Domenech, Hector Freytes & Christian de Ronde - 2009 - Mathematical Logic Quarterly 55 (3):307-319.
    In this paper we enrich the orthomodular structure by adding a modal operator, following a physical motivation. A logical system is developed, obtaining algebraic completeness and completeness with respect to a Kripkestyle semantic founded on Baer*-semigroups as in [22].
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  30.  46
    Omitting types in logic of metric structures.Ilijas Farah & Menachem Magidor - 2018 - Journal of Mathematical Logic 18 (2):1850006.
    This paper is about omitting types in logic of metric structures introduced by Ben Yaacov, Berenstein, Henson and Usvyatsov. While a complete type is omissible in some model of a countable complete...
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  31. Logic in the 1930s: Type Theory and Model Theory.Georg Schiemer & Erich H. Reck - 2013 - Bulletin of Symbolic Logic 19 (4):433-472.
    In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style ofPrincipia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early attempts (...)
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  32.  26
    Gentzen-Type Sequent Calculi for Extended Belnap–Dunn Logics with Classical Negation: A General Framework.Norihiro Kamide - 2019 - Logica Universalis 13 (1):37-63.
    Gentzen-type sequent calculi GBD+, GBDe, GBD1, and GBD2 are respectively introduced for De and Omori’s axiomatic extensions BD+, BDe, BD1, and BD2 of Belnap–Dunn logic by adding classical negation. These calculi are constructed based on a small modification of the original characteristic axiom scheme for negated implication. Theorems for syntactically and semantically embedding these calculi into a Gentzen-type sequent calculus LK for classical logic are proved. The cut-elimination, decidability, and completeness theorems for these calculi are obtained (...)
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  33.  57
    Omitting types for infinitary [ 0, 1 ] -valued logic.Christopher J. Eagle - 2014 - Annals of Pure and Applied Logic 165 (3):913-932.
    We describe an infinitary logic for metric structures which is analogous to Lω1,ω. We show that this logic is capable of expressing several concepts from analysis that cannot be expressed in finitary continuous logic. Using topological methods, we prove an omitting types theorem for countable fragments of our infinitary logic. We use omitting types to prove a two-cardinal theorem, which yields a strengthening of a result of Ben Yaacov and Iovino concerning separable quotients of Banach spaces.
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  34. Vagueness, truth and logic.Kit Fine - 1975 - Synthese 30 (3-4):265-300.
    This paper deals with the truth-Conditions and the logic for vague languages. The use of supervaluations and of classical logic is defended; and other approaches are criticized. The truth-Conditions are extended to a language that contains a definitely-Operator and that is subject to higher order vagueness.
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  35.  43
    Strong Normalizability of Typed Lambda-Calculi for Substructural Logics.Motohiko Mouri & Norihiro Kamide - 2008 - Logica Universalis 2 (2):189-207.
    The strong normalization theorem is uniformly proved for typed λ-calculi for a wide range of substructural logics with or without strong negation.
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  36.  22
    Type space functors and interpretations in positive logic.Mark Kamsma - 2023 - Archive for Mathematical Logic 62 (1):1-28.
    We construct a 2-equivalence \(\mathfrak {CohTheory}^{op }\simeq \mathfrak {TypeSpaceFunc}\). Here \(\mathfrak {CohTheory}\) is the 2-category of positive theories and \(\mathfrak {TypeSpaceFunc}\) is the 2-category of type space functors. We give a precise definition of interpretations for positive logic, which will be the 1-cells in \(\mathfrak {CohTheory}\). The 2-cells are definable homomorphisms. The 2-equivalence restricts to a duality of categories, making precise the philosophy that a theory is ‘the same’ as the collection of its type spaces (i.e. its (...)
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  37.  64
    Types of negation in logical reconstructions of meinong.Andrew Kenneth Jorgensen - 2004 - Grazer Philosophische Studien 67 (1):21-36.
    Russell's criticisms force Meinong to adopt a distinction between two types of negation. Logical expositions of Meinong's theory show the distinction is easily drawn in formal terms, but that alone does not justify the distinction intuitively.I criticise Routley'streatment of the distinction and argue that only Terence Parsons'theory retains and preserves the tight network of conceptual connections between the notions of negation, contradiction and impossibility. Hence, Parsons' approach best expresses the Meinongian perspective.
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  38. Human-Type Common Sense Needs Extensions to Logic.John McCarthy - unknown
    John McCarthy, Stanford University Logical AI (artificial intelligence) is based on programs that represent facts about the world in languages of mathematical logic and decide what actions will achieve goals by logical reasoning. A lot has been accomplished with logic as is.
     
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  39.  6
    Curry-Typed Semantics in Typed Predicate Logic.Chris Fox - 2014 - In Vit Puncochar (ed.), Logica Yearbook 2013. College Publications.
    Various questions arise in semantic analysis concerning the nature of types. These questions include whether we need types in a semantic theory, and if so, whether some version of simple type theory (STT, Church 1940) is adequate or whether a richer more flexible theory is required to capture our semantic intuitions. Propositions and propositional attitudes can be represented in an essentially untyped first-order language, provided a sufficiently rich language of terms is adopted. In the absence of rigid typing, care (...)
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  40. Reasoning About Agent Types and the Hardest Logic Puzzle Ever.Fenrong Liu & Yanjing Wang - 2013 - Minds and Machines 23 (1):123-161.
    In this paper, we first propose a simple formal language to specify types of agents in terms of necessary conditions for their announcements. Based on this language, types of agents are treated as ‘first-class citizens’ and studied extensively in various dynamic epistemic frameworks which are suitable for reasoning about knowledge and agent types via announcements and questions. To demonstrate our approach, we discuss various versions of Smullyan’s Knights and Knaves puzzles, including the Hardest Logic Puzzle Ever (HLPE) proposed by (...)
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  41.  24
    An Omitting Types Theorem for first order logic with infinitary relation symbols.Tarek Sayed Ahmed & Basim Samir - 2007 - Mathematical Logic Quarterly 53 (6):564-570.
    In this paper, an extension of first order logic is introduced. In such logics atomic formulas may have infinite lengths. An Omitting Types Theorem is proved.
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  42.  12
    Unification types in logic.Wojciech Dzik - 2007 - Katowice: Wydawnictwo Uniwersytetu Śląskiego.
  43.  30
    Erratum to: Grammar Induction by Unification of Type-logical Lexicons. [REVIEW]Sean A. Fulop - 2011 - Journal of Logic, Language and Information 20 (1):135-136.
  44. After Godel: Platonism and Rationalism in Mathematics and Logic.Richard L. Tieszen - 2011 - Oxford, England: Oxford University Press UK.
    Richard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Gödel's writings on the philosophy and foundations of mathematics and logic. Tieszen structures the argument around Gödel's three philosophical heroes - Plato, Leibniz, and Husserl - and his engagement with Kant, and supplements close readings of Gödel's texts on foundations with materials from Gödel's Nachlass and from Hao Wang's discussions with Gödel. He provides discussions of Gödel's views, and develops a new type (...)
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  45. The logic of indirect speech.Steven Pinker - manuscript
    When people speak, they often insinuate their intent indirectly rather than stating it as a bald proposition. Examples include sexual come-ons, veiled threats, polite requests, and concealed bribes. We propose a three-part theory of indirect speech, based on the idea that human communication involves a mixture of cooperation and conflict. First, indirect requests allow for plausible deniability, in which a cooperative listener can accept the request, but an uncooperative one cannot react adversarially to it. This intuition is sup- ported by (...)
     
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  46.  43
    Omitting types in fuzzy logic with evaluated syntax.Petra Murinová & Vilém Novák - 2006 - Mathematical Logic Quarterly 52 (3):259-268.
    This paper is a contribution to the development of model theory of fuzzy logic in narrow sense. We consider a formal system EvŁ of fuzzy logic that has evaluated syntax, i. e. axioms need not be fully convincing and so, they form a fuzzy set only. Consequently, formulas are provable in some general degree. A generalization of Gödel's completeness theorem does hold in EvŁ. The truth values form an MV-algebra that is either finite or Łukasiewicz algebra on [0, (...)
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  47.  23
    Combinatory Logic: Pure, Applied and Typed.Katalin Bimbó - 2011 - Taylor & Francis.
    Reader-friendly without compromising the precision of exposition, the book includes many new research results not found in the available literature.
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  48.  78
    Resolution in type theory.Peter B. Andrews - 1971 - Journal of Symbolic Logic 36 (3):414-432.
  49.  85
    Glivenko type theorems for intuitionistic modal logics.Guram Bezhanishvili - 2001 - Studia Logica 67 (1):89-109.
    In this article we deal with Glivenko type theorems for intuitionistic modal logics over Prior's MIPC. We examine the problems which appear in proving Glivenko type theorems when passing from the intuitionistic propositional logic Intto MIPC. As a result we obtain two different versions of Glivenko's theorem for logics over MIPC. Since MIPCcan be thought of as a one-variable fragment of the intuitionistic predicate logic Q-Int, one of the versions of Glivenko's theorem for logics over MIPCis (...)
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  50. Schönfinkel-type Operators for Classical Logic.Katalin Bimbó - 2010 - Studia Logica 95 (3):355-378.
    We briefly overview some of the historical landmarks on the path leading to the reduction of the number of logical connectives in classical logic. Relying on the duality inherent in Boolean algebras, we introduce a new operator ( Nallor ) that is the dual of Schönfinkel’s operator. We outline the proof that this operator by itself is sufficient to define all the connectives and operators of classical first-order logic ( Fol ). Having scrutinized the proof, we pinpoint the (...)
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