-
28A Proof-Theoretic Semantics for Adjectival ModificationJournal of Logic, Language and Information 26 (1): 21-43. 2017.The paper introduces a proof-theoretic semantics for adjectival modification as an alternative to the traditional model-theoretic semantics basing meaning on truth-conditions. The paper considers the proof-theoretic meaning of modification by means of the three traditional adjective classes: intersective, subsective and privative. It does so by introducing a meaning-conferring natural-deduction proof system for such modification. The PTS theory of meaning is not polluted by ontological commitmen…Read more
-
202Proof-theoretic semantics for a natural language fragmentLinguistics and Philosophy 33 (6): 447-477. 2010.The paper presents a proof-theoretic semantics (PTS) for a fragment of natural language, providing an alternative to the traditional model-theoretic (Montagovian) semantics (MTS), whereby meanings are truth-condition (in arbitrary models). Instead, meanings are taken as derivability-conditions in a dedicated natural-deduction (ND) proof-system. This semantics is effective (algorithmically decidable), adhering to the meaning as use paradigm, not suffering from several of the criticisms formulated…Read more
-
75Categorial grammar and the semantics of contextual prepositional phrasesLinguistics and Philosophy 29 (4). 2006.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 expect…Read more
-
70Plurality and temporal modificationLinguistics and Philosophy 29 (3). 2006.A semantics with plural entitles and plural times accounts for cumulative relations between plural arguments and temporal expressions. The semantics equips nominal, verbal and sentential meanings with temporal context variables and treats temporal modifiers as temporal generalized quantifiers; cumulative conjunction, however, takes place at types lower than generalized quantifiers. The mediation of temporal context variables allows cumulative relations to percolate between an argument in a main …Read more
-
29A Lambek AutomatonLogic Journal of the IGPL 14 (5): 659-708. 2006.We define an automata-theoretic counterpart of grammars based on the Lambek-calculus L, a prominent formalism in computational linguistics. While the usual push-down automaton has the same weak generative power as the L-based grammars , there is no direct relationship between the computations of a PDA for some language L and the derivations of an L-based grammar for L. In the Lambek-automaton, on the other hand, there is a tight relation between automaton computations and grammar derivations. Th…Read more
-
109Unification grammars and off-line parsabilityJournal of Logic, Language and Information 14 (2): 199-234. 2005.Unification grammars are known to be Turing-equivalent; given a grammar G and a word w, it is undecidable whether w L(G). In order to ensure decidability, several constraints on grammars, commonly known as off-line parsability (OLP), were suggested, such that the recognition problem is decidable for grammars which satisfy OLP. An open question is whether it is decidable if a given grammar satisfies OLP. In this paper we investigate various definitions of OLP and discuss their interrelations, pro…Read more
-
62Harmony in Multiple-Conclusion Natural-DeductionLogica Universalis 8 (2): 215-259. 2014.The paper studies the extension of harmony and stability, major themes in proof-theoretic semantics, from single-conclusion natural-deduction systems to multiple -conclusions natural-deduction, independently of classical logic. An extension of the method of obtaining harmoniously-induced general elimination rules from given introduction rules is suggested, taking into account sub-structurality. Finally, the reductions and expansions of the multiple -conclusions natural-deduction representation o…Read more
-
13A proof-theoretic universal property of determinersJournal of Applied Logic 13 (4): 799-808. 2015.
-
70Bilattices and the semantics of natural language questionsLinguistics and Philosophy 25 (1): 37-64. 2002.In this paper we reexamine the question of whether questions areinherently intensional entities. We do so by proposing a novelextensional theory of questions, based on a re-interpretation of thedomain of t as a bilattice rather than the usual booleaninterpretation. We discuss the adequacy of our theory with respect tothe adequacy criteria imposed on the semantics of questionsby (Groenendijk and Stokhof 1997). We show that the theory is able to account in astraightforward manner for some complex …Read more
-
827Proof-Theoretic Semantics for Subsentential PhrasesStudia Logica 94 (3): 381-401. 2010.The paper briefly surveys the sentential proof-theoretic semantics for fragment of English. Then, appealing to a version of Frege’s context-principle (specified to fit type-logical grammar), a method is presented for deriving proof-theoretic meanings for sub-sentential phrases, down to lexical units (words). The sentential meaning is decomposed according to the function-argument structure as determined by the type-logical grammar. In doing so, the paper presents a novel proof-theoretic interpret…Read more
-
23Contrastive LogicLogic Journal of the IGPL 3 (5): 725-744. 1995.In this paper I introduce the notion of bilogics, namely logics interpreted over a pair of structures, in contrast to classical logic and many of its variations, the formulae of which are interpreted over one structure. In particular, I introduce and study Contrastive Logic, suitable for expressing contrast and conformity between the two structures involved.A major reason for this study is striving towards an extension of truth-conditional semantics to cover several natural-language particles, w…Read more
-
68A Logic Inspired by Natural Language: Quantifiers As SubnectorsJournal of Philosophical Logic 43 (6): 1153-1172. 2014.Inspired by the grammar of natural language, the paper presents a variant of first-order logic, in which quantifiers are not sentential operators, but are used as subnectors . A quantified term formed by a subnector is an argument of a predicate. The logic is defined by means of a meaning-conferring natural-deduction proof-system, according to the proof-theoretic semantics program. The harmony of the I/E-rules is shown. The paper then presents a translation, called the Frege translation, from th…Read more
-
40Off-line parsability and the well-foundedness of subsumptionJournal of Logic, Language and Information 8 (1): 1-16. 1999.Typed feature structures are used extensively for the specification of linguistic information in many formalisms. The subsumption relation orders TFSs by their information content. We prove that subsumption of acyclic TFSs is well founded, whereas in the presence of cycles general TFS subsumption is not well founded. We show an application of this result for parsing, where the well-foundedness of subsumption is used to guarantee termination for grammars that are off-line parsable. We define a ne…Read more
-
44Relational Semantics of the Lambek Calculus Extended with Classical Propositional LogicStudia Logica 102 (3): 479-497. 2014.We show that the relational semantics of the Lambek calculus, both nonassociative and associative, is also sound and complete for its extension with classical propositional logic. Then, using filtrations, we obtain the finite model property for the nonassociative Lambek calculus extended with classical propositional logic
-
29On a Distinction of Two Facets of Meaning and its Role in Proof-theoretic SemanticsLogica Universalis 9 (1): 121-127. 2015.I show that in the context of proof-theoretic semantics, Dummett’s distinction between the assertoric meaning of a sentence and its ingredient sense can be seen as a distinction between two proof-theoretic meanings of a sentence: 1.Meaning as a conclusion of an introduction rule in a meaning-conferring natural-deduction proof system. 2.Meaning as a premise of an introduction rule in a meaning-conferring natural-deduction proof system. The effect of this distinction on compositionality of proof-t…Read more
-
87Bilateralism in Proof-Theoretic SemanticsJournal of Philosophical Logic (2-3): 1-21. 2013.The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between (positive) introduction and elimination rules traditionally imposed by harmony,…Read more
-
73Temporal prepositions and temporal generalized quantifiersLinguistics and Philosophy 24 (2): 187-222. 2001.In this paper, we show how the problem of accounting for the semanticsof temporal preposition phrases (tPPs) leads us to some surprisinginsights into the semantics of temporal expressions ingeneral. Specifically, we argue that a systematic treatment of EnglishtPPs is greatly facilitated if we endow our meaning assignments with context variables, a device which allows a tPP to restrict domainsof quantification arising elsewhere in a sentence. We observe that theuse of context variables implies th…Read more
-
76Proof-theoretic semantic values for logical operatorsReview of Symbolic Logic 4 (3): 466-478. 2011.The paper proposes a semantic value for the logical constants (connectives and quantifiers) within the framework of proof-theoretic semantics, basic meaning on the introduction rules of a meaning conferring natural deduction proof system. The semantic value is defined based on Fregecontributions” to sentential meanings as determined by the function-argument structure as induced by a type-logical grammar. In doing so, the paper proposes a novel proof-theoretic interpretation of the semantic types…Read more
-
47Commutation-Augmented Pregroup Grammars and Mildly Context-Sensitive LanguagesStudia Logica 87 (2-3): 295-321. 2007.The paper presents a generalization of pregroup, by which a freely-generated pregroup is augmented with a finite set of commuting inequations, allowing limited commutativity and cancelability. It is shown that grammars based on the commutation-augmented pregroups generate mildly context-sensitive languages. A version of Lambek’s switching lemma is established for these pregroups. Polynomial parsability and semilinearity are shown for languages generated by these grammars.
-
446A Note on HarmonyJournal of Philosophical Logic 41 (3): 613-628. 2012.In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivatio…Read more
-
82A 'natural logic' inference system using the Lambek calculusJournal of Logic, Language and Information 15 (3): 273-295. 2006.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 Hille…Read more
Areas of Specialization
Philosophy of Language |
Logic and Philosophy of Logic |
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Language |
Philosophy of Mathematics |