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  1. Tree Models and (Labeled) Categorial Grammar.Yde Venema - 1996 - Journal of Logic, Language and Information 5 (3-4):253-277.
    This paper studies the relation between some extensions of the non-associative Lambek Calculus NL and their interpretation in tree models (free groupoids). We give various examples of sequents that are valid in tree models, but not derivable in NL. We argue why tree models may not be axiomatizable if we add finitely many derivation rules to NL, and proceed to consider labeled calculi instead.We define two labeled categorial calculi, and prove soundness and completeness for interpretations that are almost the intended (...)
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  • Parsing Pregroup Grammars and Lambek Calculus Using Partial Composition.Denis Béchet - 2007 - Studia Logica 87 (2-3):199-224.
    The paper presents a way to transform pregroup grammars into contextfree grammars using functional composition. The same technique can also be used for the proof-nets of multiplicative cyclic linear logic and for Lambek calculus allowing empty premises.
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  • Intuitionistic Categorial Grammar.Aarne Ranta - 1991 - Linguistics and Philosophy 14 (2):203 - 239.
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  • Raising as Function Composition.Pauline Jacobson - 1990 - Linguistics and Philosophy 13 (4):423 - 475.
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  • Intensionality and Boundedness.Glyn Morrill - 1990 - Linguistics and Philosophy 13 (6):699 - 726.
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  • Language in Action.Johan Benthem - 1991 - Journal of Philosophical Logic 20 (3):225 - 263.
    A number of general points behind the story of this paper may be worth setting out separately, now that we have come to the end.There is perhaps one obvious omission to be addressed right away. Although the word “information” has occurred throughout this paper, it must have struck the reader that we have had nothing to say on what information is. In this respect, our theories may be like those in physics: which do not explain what “energy” is (a notion (...)
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  • On the Completeness of the Lambek Calculus with Respect to Relativized Relational Semantics.Nikolai Pankrat'ev - 1994 - Journal of Logic, Language and Information 3 (3):233-246.
    Recently M. Szabolcs [12] has shown that many substructural logics including Lambek CalculusL are complete with respect to relativized Relational Semantics. The current paper proves that it is sufficient forL to consider a relativization to the relation x dividesy in some fixed semigroupG.
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  • Fibred Semantics for Feature-Based Grammar Logic.Jochen Dörre, Esther König & Dov Gabbay - 1996 - Journal of Logic, Language and Information 5 (3-4):387-422.
    This paper gives a simple method for providing categorial brands of feature-based unification grammars with a model-theoretic semantics. The key idea is to apply the paradigm of fibred semantics (or layered logics, see Gabbay (1990)) in order to combine the two components of a feature-based grammar logic. We demonstrate the method for the augmentation of Lambek categorial grammar with Kasper/Rounds-style feature logic. These are combined by replacing (or annotating) atomic formulas of the first logic, i.e. the basic syntactic types, by (...)
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  • Gapping as Constituent Coordination.Mark J. Steedman - 1990 - Linguistics and Philosophy 13 (2):207 - 263.
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  • New Directions in Type-Theoretic Grammars.Reinhard Muskens - 2010 - Journal of Logic, Language and Information 19 (2):129-136.
    This paper argues for the idea that in describing language we should follow Haskell Curry in distinguishing between the structure of an expression and its appearance or manifestation . It is explained how making this distinction obviates the need for directed types in type-theoretic grammars and a simple grammatical formalism is sketched in which representations at all levels are lambda terms. The lambda term representing the abstract structure of an expression is homomorphically translated to a lambda term representing its manifestation, (...)
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  • Semantic Vector Models and Functional Models for Pregroup Grammars.Anne Preller & Mehrnoosh Sadrzadeh - 2011 - Journal of Logic, Language and Information 20 (4):419-443.
    We show that vector space semantics and functional semantics in two-sorted first order logic are equivalent for pregroup grammars. We present an algorithm that translates functional expressions to vector expressions and vice-versa. The semantics is compositional, variable free and invariant under change of order or multiplicity. It includes the semantic vector models of Information Retrieval Systems and has an interior logic admitting a comprehension schema. A sentence is true in the interior logic if and only if the ‘usual’ first order (...)
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  • From Word to Sentence: A Pregroup Analysis of the Object Pronoun Who ( M ). [REVIEW]J. Lambek - 2007 - Journal of Logic, Language and Information 16 (3):303-323.
    We explore a computational algebraic approach to grammar via pregroups, that is, partially ordered monoids in which each element has both a left and a right adjoint. Grammatical judgements are formed with the help of calculations on types. These are elements of the free pregroup generated by a partially ordered set of basic types, which are assigned to words, here of English. We concentrate on the object pronoun who(m).
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  • Lambek Calculus and its Relational Semantics: Completeness and Incompleteness. [REVIEW]Hajnal Andréka & Szabolcs Mikulás - 1994 - Journal of Logic, Language and Information 3 (1):1-37.
    The problem of whether Lambek Calculus is complete with respect to (w.r.t.) relational semantics, has been raised several times, cf. van Benthem (1989a) and van Benthem (1991). In this paper, we show that the answer is in the affirmative. More precisely, we will prove that that version of the Lambek Calculus which does not use the empty sequence is strongly complete w.r.t. those relational Kripke-models where the set of possible worlds,W, is a transitive binary relation, while that version of the (...)
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  • The Competence-Performance Distinction in Mental Philosophy.Raymond J. Nelson - 1978 - Synthese 39 (November):337-382.
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  • Discontinuity in Categorial Grammar.Glyn Morrill - 1995 - Linguistics and Philosophy 18 (2):175 - 219.
    Discontinuity refers to the character of many natural language constructions wherein signs differ markedly in their prosodic and semantic forms. As such it presents interesting demands on monostratal computational formalisms which aspire to descriptive adequacy. Pied piping, in particular, is argued by Pollard (1988) to motivate phrase structure-style feature percolation. In the context of categorial grammar, Bach (1981, 1984), Moortgat (1988, 1990, 1991) and others have sought to provide categorial operators suited to discontinuity. These attempts encounter certain difficulties with respect (...)
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  • On the Logic of Β -Pregroups.Aleksandra Kiślak-Malinowska - 2007 - Studia Logica 87 (2-3):323 - 342.
    In this paper we concentrate mainly on the notion of β-pregroups, which are pregroups (first introduced by Lambek [18] in 1999) enriched with modality operators. β-pregroups were first proposed by Fadda [11] in 2001. The motivation to introduce them was to limit (locally) the associativity in the calculus considered. In this paper we present this new calculus in the form of a rewriting system, prove the very important feature of this system - that in a given derivation the non- expanding (...)
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  • Semantic Bootstrapping of Type-Logical Grammar.Sean A. Fulop - 2005 - 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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  • Infinitary Action Logic: Complexity, Models and Grammars.Wojciech Buszkowski & Ewa Palka - 2008 - Studia Logica 89 (1):1-18.
    Action logic of Pratt [21] can be presented as Full Lambek Calculus FL [14, 17] enriched with Kleene star *; it is equivalent to the equational theory of residuated Kleene algebras (lattices). Some results on axiom systems, complexity and models of this logic were obtained in [4, 3, 18]. Here we prove a stronger form of *-elimination for the logic of *-continuous action lattices and the –completeness of the equational theories of action lattices of subsets of a finite monoid and (...)
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  • Meaning and Interpretation. II.Urszula Wybraniec-Skardowska - 2007 - Studia Logica 85 (2):261-274.
    The paper enriches the conceptual apparatus of the theory of meaning and denotation that was presented in Part I (Section 3). This part concentrates on the notion of interpretation, which is defined as an equivalence class of the relation possessing the same manner of interpreting types. In this part, some relations between meaning and interpretation, as well as one between denotation an interpretational denotation are established. In the theory of meaning and interpretation, the notion of language communication has been formally (...)
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  • Meaning and Interpretation. I.Urszula Wybraniec-Skardowska - 2007 - Studia Logica 85 (1):105-132.
    The paper is an attempt at a logical explication of some crucial notions of current general semantics and pragmatics. A general, axiomatic, formal-logical theory of meaning and interpretation is outlined in this paper.In the theory, accordingto the token-type distinction of Peirce, language is formalised on two levels: first as a language of token-objects (understood as material, empirical, enduring through time-and space objects) and then – as a language of type-objects (understood as abstract objects, as classes of tokens). The basic concepts (...)
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  • Categorial Grammar and the Semantics of Contextual Prepositional Phrases.Nissim Francez & Mark Steedman - 2006 - Linguistics and Philosophy 29 (4):381 - 417.
    The paper proposes a semantics for contextual (i.e., Temporal and Locative) Prepositional Phrases (CPPs) like during every meeting, in the garden, when Harry met Sally and where I’m calling from. The semantics is embodied in a multi-modal extension of Combinatory Categoral Grammar (CCG). The grammar allows the strictly monotonic compositional derivation of multiple correct interpretations for “stacked” or multiple CPPs, including interpretations whose scope relations are not what would be expected on standard assumptions about surfacesyntactic command and monotonic derivation. A (...)
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  • A 'Natural Logic' Inference System Using the Lambek Calculus.Anna Zamansky, Nissim Francez & Yoad Winter - 2006 - Journal of Logic, Language and Information 15 (3):273-295.
    This paper develops an inference system for natural language within the ‘Natural Logic’ paradigm as advocated by van Benthem, Sánchez and others. The system that we propose is based on the Lambek calculus and works directly on the Curry-Howard counterparts for syntactic representations of natural language, with no intermediate translation to logical formulae. The Lambek -based system we propose extends the system by Fyodorov et~al., which is based on the Ajdukiewicz/Bar-Hillel calculus Bar Hillel,. This enables the system to deal with (...)
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  • Dynamic Dependency Grammar.David Milward - 1994 - Linguistics and Philosophy 17 (6):561 - 605.
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  • Term-Labeled Categorial Type Systems.Richard T. Oehrle - 1994 - Linguistics and Philosophy 17 (6):633 - 678.
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  • Logical Conceptualization of Knowledge on the Notion of Language Communication.Urszula Wybraniec-Skardowska - 2017 - Studies in Logic, Grammar and Rhetoric 52 (1):247-269.
    The main objective of the paper is to provide a conceptual apparatus of a general logical theory of language communication. The aim of the paper is to outline a formal-logical theory of language in which the concepts of the phenomenon of language communication and language communication in general are defined and some conditions for their adequacy are formulated. The theory explicates the key notions of contemporary syntax, semantics, and pragmatics. The theory is formalized on two levels: token-level and type-level. As (...)
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  • Infinity and the Foundations of Linguistics.Ryan M. Nefdt - 2019 - Synthese 196 (5):1671-1711.
    The concept of linguistic infinity has had a central role to play in foundational debates within theoretical linguistics since its more formal inception in the mid-twentieth century. The conceptualist tradition, marshalled in by Chomsky and others, holds that infinity is a core explanandum and a link to the formal sciences. Realism/Platonism takes this further to argue that linguistics is in fact a formal science with an abstract ontology. In this paper, I argue that a central misconstrual of formal apparatus of (...)
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  • O expressivismo lógico de Aristóteles segundo Lucas Angioni: um breve e introdutório quadro teórico.Aislan Fernandes Pereira - 2017 - Books of Abstracts (3rd FILOMENA Workshop).
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  • Separating Syntax and Combinatorics in Categorial Grammar.Reinhard Muskens - 2007 - Research on Language and Computation 5 (3):267-285.
    The ‘syntax’ and ‘combinatorics’ of my title are what Curry (1961) referred to as phenogrammatics and tectogrammatics respectively. Tectogrammatics is concerned with the abstract combinatorial structure of the grammar and directly informs semantics, while phenogrammatics deals with concrete operations on syntactic data structures such as trees or strings. In a series of previous papers (Muskens, 2001a; Muskens, 2001b; Muskens, 2003) I have argued for an architecture of the grammar in which finite sequences of lambda terms are the basic data structures, (...)
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  • Judgement Aggregation in Non-Classical Logics.Daniele Porello - 2017 - Journal of Applied Non-Classical Logics 27 (1-2):106-139.
    This work contributes to the theory of judgement aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgement aggregation to cope with non-classical logics, we discuss in particular results for the case of Intuitionistic Logic, the Lambek calculus, Linear Logic and Relevant Logics. The motivation for studying judgement aggregation in non-classical logics is that they offer a number of modelling choices to represent agents’ reasoning in aggregation problems. By studying judgement aggregation in logics that (...)
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  • The Displacement Calculus.Glyn Morrill, Oriol Valentín & Mario Fadda - 2011 - Journal of Logic, Language and Information 20 (1):1-48.
    If all dependent expressions were adjacent some variety of immediate constituent analysis would suffice for grammar, but syntactic and semantic mismatches are characteristic of natural language; indeed this is a, or the, central problem in grammar. Logical categorial grammar reduces grammar to logic: an expression is well-formed if and only if an associated sequent is a theorem of a categorial logic. The paradigmatic categorial logic is the Lambek calculus, but being a logic of concatenation the Lambek calculus can only capture (...)
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  • 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 with an (...)
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  • Monoidal Logics: Completeness and Classical Systems.Clayton Peterson - 2019 - Journal of Applied Non-Classical Logics 29 (2):121-151.
    ABSTRACTMonoidal logics were introduced as a foundational framework to analyze the proof theory of logical systems. Inspired by Lambek's seminal work in categorical logic, the objective is to defin...
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  • Modal Logic as Metalogic.Kosta Došen - 1992 - Journal of Logic, Language and Information 1 (3):173-201.
    The goal of this paper is to show how modal logic may be conceived as recording the derived rules of a logical system in the system itself. This conception of modal logic was propounded by Dana Scott in the early seventies. Here, similar ideas are pursued in a context less classical than Scott's.First a family of propositional logical systems is considered, which is obtained by gradually adding structural rules to a variant of the nonassociative Lambek calculus. In this family one (...)
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  • Modal Translations in Substructural Logics.Kosta Došen - 1992 - Journal of Philosophical Logic 21 (3):283 - 336.
    Substructural logics are logics obtained from a sequent formulation of intuitionistic or classical logic by rejecting some structural rules. The substructural logics considered here are linear logic, relevant logic and BCK logic. It is proved that first-order variants of these logics with an intuitionistic negation can be embedded by modal translations into S4-type extensions of these logics with a classical, involutive, negation. Related embeddings via translations like the double-negation translation are also considered. Embeddings into analogues of S4 are obtained with (...)
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  • On Language Adequacy.Urszula Wybraniec-Skardowska - 2015 - Studies in Logic, Grammar and Rhetoric 40 (1):257-292.
    The paper concentrates on the problem of adequate reflection of fragments of reality via expressions of language and inter-subjective knowledge about these fragments, called here, in brief, language adequacy. This problem is formulated in several aspects, the most being: the compatibility of language syntax with its bi-level semantics: intensional and extensional. In this paper, various aspects of language adequacy find their logical explication on the ground of the formal-logical theory T of any categorial language L generated by the so-called classical (...)
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  • On the Recognizing Power of the Lambek Calculus with Brackets.Makoto Kanazawa - 2018 - Journal of Logic, Language and Information 27 (4):295-312.
    Every language recognized by the Lambek calculus with brackets is context-free. This is shown by combining an observation by Jäger with an entirely straightforward adaptation of the method Pentus used for the original Lambek calculus. The case of the variant of the calculus allowing sequents with empty antecedents is slightly more complicated, requiring a restricted use of the multiplicative unit.
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  • Lower Semilattice-Ordered Residuated Semigroups and Substructural Logics.Szabolcs Mikulás - 2015 - Studia Logica 103 (3):453-478.
    We look at lower semilattice-ordered residuated semigroups and, in particular, the representable ones, i.e., those that are isomorphic to algebras of binary relations. We will evaluate expressions in representable algebras and give finite axiomatizations for several notions of validity. These results will be applied in the context of substructural logics.
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  • Connexive Conditional Logic. Part I.Heinrich Wansing & Matthias Unterhuber - forthcoming - Logic and Logical Philosophy:1.
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  • Lambek Vs. Lambek: Functorial Vector Space Semantics and String Diagrams for Lambek Calculus.Bob Coecke, Edward Grefenstette & Mehrnoosh Sadrzadeh - 2013 - Annals of Pure and Applied Logic 164 (11):1079-1100.
    The Distributional Compositional Categorical model is a mathematical framework that provides compositional semantics for meanings of natural language sentences. It consists of a computational procedure for constructing meanings of sentences, given their grammatical structure in terms of compositional type-logic, and given the empirically derived meanings of their words. For the particular case that the meaning of words is modelled within a distributional vector space model, its experimental predictions, derived from real large scale data, have outperformed other empirically validated methods that (...)
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  • Extending Lambek Grammars to Basic Categorial Grammars.Wojciech Buszkowski - 1996 - Journal of Logic, Language and Information 5 (3-4):279-295.
    Pentus (1992) proves the equivalence of LCG's and CFG's, and CFG's are equivalent to BCG's by the Gaifman theorem (Bar-Hillel et al., 1960). This paper provides a procedure to extend any LCG to an equivalent BCG by affixing new types to the lexicon; a procedure of that kind was proposed as early, as Cohen (1967), but it was deficient (Buszkowski, 1985). We use a modification of Pentus' proof and a new proof of the Gaifman theorem on the basis of the (...)
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  • Grammar Logicised: Relativisation.Glyn Morrill - 2017 - Linguistics and Philosophy 40 (2):119-163.
    Many variants of categorial grammar assume an underlying logic which is associative and linear. In relation to left extraction, the former property is challenged by island domains, which involve nonassociativity, and the latter property is challenged by parasitic gaps, which involve nonlinearity. We present a version of type logical grammar including ‘structural inhibition’ for nonassociativity and ‘structural facilitation’ for nonlinearity and we give an account of relativisation including islands and parasitic gaps and their interaction.
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  • Husserl's Logical Grammar.Ansten Klev - 2018 - History and Philosophy of Logic 39 (3):232-269.
    Lecture notes from Husserl's logic lectures published during the last 20 years offer a much better insight into his doctrine of the forms of meaning than does the fourth Logical Investigation or any other work published during Husserl's lifetime. This paper provides a detailed reconstruction, based on all the sources now available, of Husserl's system of logical grammar. After having explained the notion of meaning that Husserl assumes in his later logic lectures as well as the notion of form of (...)
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  • A Comparison Between Monoidal and Substructural Logics.Clayton Peterson - 2016 - Journal of Applied Non-Classical Logics 26 (2):126-159.
    Monoidal logics were introduced as a foundational framework to analyse the proof theory of deontic logic. Building on Lambek’s work in categorical logic, logical systems are defined as deductive systems, that is, as collections of equivalence classes of proofs satisfying specific rules and axiom schemata. This approach enables the classification of deductive systems with respect to their categorical structure. When looking at their proof theory, however, one can see that there are similarities between monoidal and substructural logics. The purpose of (...)
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  • Non-Normal Modalities in Variants of Linear Logic.D. Porello & N. Troquard - 2015 - Journal of Applied Non-Classical Logics 25 (3):229-255.
    This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of linear logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic linear logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class of Kripke resource models (...)
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  • Trivalent Logics Arising From L-Models for the Lambek Calculus with Constants.S. L. Kuznetsov - 2014 - Journal of Applied Non-Classical Logics 24 (1-2):132-137.
    We consider language models for the Lambek calculus that allow empty antecedents and enrich them with constants for the empty language and for the language containing only the empty word. No complete calculi are known with respect to these semantics, and in this paper we consider several trivalent systems that arise as fragments of these models? logics.
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  • Quine's Philosophy of Language and Polish Logic.Eli Dresner - 1999 - History and Philosophy of Logic 20 (2):79-96.
    The Polish logicians' propositional calculi, which consist in a distinct synthesis of the Fregean and Boolean approaches to logic, influenced W. V. Quine's early work in formal logic. This early formal work of Quine's, in turn, can be shown to serve as one of the sources of his holistic conception of natural language.
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  • Head or Tail? De Morgan on the Bounds of Traditional Logic.Víctor Sánchez Valencia - 1997 - History and Philosophy of Logic 18 (3):123-138.
    This paper is concerned with De Morgan?s explanation of the validity of arguments that involve relational notions. It discusses De Morgan?s expansion of traditional logic aimed at accommodating those inferences, and makes the point that his endeavour is not successful in that the rules that made up his new logic are not sound. Nevertheless, the most important scholarly work on De Morgan?s logic, and contrary to that De Morgan?s mistake is not beyond repair. The rules that determine his new logic (...)
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  • Multimodal Linguistic Inference.Michael Moortgat - 1996 - Journal of Logic, Language and Information 5 (3-4):349-385.
    In this paper we compare grammatical inference in the context of simple and of mixed Lambek systems. Simple Lambek systems are obtained by taking the logic of residuation for a family of multiplicative connectives /,,\, together with a package of structural postulates characterizing the resource management properties of the connective.Different choices for Associativity and Commutativity yield the familiar logics NL, L, NLP, LP. Semantically, a simple Lambek system is a unimodal logic: the connectives get a Kripke style interpretation in terms (...)
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  • Symmetric Categorial Grammar.Michael Moortgat - 2009 - Journal of Philosophical Logic 38 (6):681-710.
    The Lambek-Grishin calculus is a symmetric version of categorial grammar obtained by augmenting the standard inventory of type-forming operations (product and residual left and right division) with a dual family: coproduct, left and right difference. Interaction between these two families is provided by distributivity laws. These distributivity laws have pleasant invariance properties: stability of interpretations for the Curry-Howard derivational semantics, and structure-preservation at the syntactic end. The move to symmetry thus offers novel ways of reconciling the demands of natural language (...)
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  • An Extension of the Formulas-as-Types Paradigm.J. Lambek - 1997 - Dialogue 36 (1):33-.
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