38 found
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  1. Mathematical Linguistics and Proof Theory.Wojciech Buszkowski - 1997 - In Benthem & Meulen (eds.), Handbook of Logic and Language. MIT Press. pp. 683--736.
     
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  2.  24
    Completeness Results for Lambek Syntactic Calculus.Wojciech Buszkowski - 1986 - Mathematical Logic Quarterly 32 (1‐5):13-28.
  3.  25
    Completeness Results for Lambek Syntactic Calculus.Wojciech Buszkowski - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (1-5):13-28.
  4.  14
    Some Decision Problems in the Theory of Syntactic Categories.Wojciech Buszkowski - 1982 - Mathematical Logic Quarterly 28 (33‐38):539-548.
  5.  27
    Some Decision Problems in the Theory of Syntactic Categories.Wojciech Buszkowski - 1982 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 28 (33-38):539-548.
  6.  35
    Categorial Grammars Determined From Linguistic Data by Unification.Wojciech BuszKowski & Gerald Penn - 1990 - Studia Logica 49 (4):431 - 454.
    We provide an algorithm for determining a categorial grammar from linguistic data that essentially uses unification of type-schemes assigned to atoms. The algorithm presented here extends an earlier one restricted to rigid categorial grammars, introduced in [4] and [5], by admitting non-rigid outputs. The key innovation is the notion of an optimal unifier, a natural generalization of that of a most general unifier.
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  7.  27
    The Finite Model Property for BCI and Related Systems.Wojciech Buszkowski - 1996 - Studia Logica 57 (2-3):303 - 323.
    We prove the finite model property (fmp) for BCI and BCI with additive conjunction, which answers some open questions in Meyer and Ono [11]. We also obtain similar results for some restricted versions of these systems in the style of the Lambek calculus [10, 3]. The key tool is the method of barriers which was earlier introduced by the author to prove fmp for the product-free Lambek calculus [2] and the commutative product-free Lambek calculus [4].
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  8.  7
    Sequent Systems for Compact Bilinear Logic.Wojciech Buszkowski - 2003 - Mathematical Logic Quarterly 49 (5):467.
    Compact Bilinear Logic , introduced by Lambek [14], arises from the multiplicative fragment of Noncommutative Linear Logic of Abrusci [1] by identifying times with par and 0 with 1. In this paper, we present two sequent systems for CBL and prove the cut-elimination theorem for them. We also discuss a connection between cut-elimination for CBL and the Switching Lemma from [14].
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  9.  57
    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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  10.  3
    Involutive Nonassociative Lambek Calculus: Sequent Systems and Complexity.Wojciech Buszkowski - 2017 - Bulletin of the Section of Logic 46 (1/2).
    In [5] we study Nonassociative Lambek Calculus augmented with De Morgan negation, satisfying the double negation and contraposition laws. This logic, introduced by de Grooté and Lamarche [10], is called Classical Non-Associative Lambek Calculus. Here we study a weaker logic InNL, i.e. NL with two involutive negations. We present a one-sided sequent system for InNL, admitting cut elimination. We also prove that InNL is PTIME.
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  11.  22
    Finite Models of Some Substructural Logics.Wojciech Buszkowski - 2002 - Mathematical Logic Quarterly 48 (1):63-72.
    We give a proof of the finite model property of some fragments of commutative and noncommutative linear logic: the Lambek calculus, BCI, BCK and their enrichments, MALL and Cyclic MALL. We essentially simplify the method used in [4] for proving fmp of BCI and the Lambek ca culus and in [5] for proving fmp of MALL. Our construction of finite models also differs from that used in Lafont [8] in his proof of fmp of MALL.
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  12.  2
    The Logic of Types.Wojciech Buszkowski - 1987 - In Jan T. J. Srzednicki (ed.), Initiatives in Logic. M. Nijhoff. pp. 180--206.
  13.  18
    Presuppositional Completeness.Wojciech Buszkowski - 1989 - Studia Logica 48 (1):23 - 34.
    Some notions of the logic of questions (presupposition of a question, validation, entailment) are used for defining certain kinds of completeness of elementary theories. Presuppositional completeness, closely related to -completeness ([3], [6]), is shown to be fulfilled by strong elementary theories like Peano arithmetic.
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  14.  18
    Undecidability of Some Logical Extensions of Ajdukiewicz-Lambek Calculus.Wojciech Buszkowski - 1978 - Studia Logica 37 (1):59 - 64.
  15.  20
    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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  16.  30
    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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  17.  53
    Gaifman's Theorem on Categorial Grammars Revisited.Wojciech Buszkowski - 1988 - Studia Logica 47 (1):23 - 33.
    The equivalence of (classical) categorial grammars and context-free grammars, proved by Gaifman [4], is a very basic result of the theory of formal grammars (an essentially equivalent result is known as the Greibach normal form theorem [1], [14]). We analyse the contents of Gaifman's theorem within the framework of structure and type transformations. We give a new proof of this theorem which relies on the algebra of phrase structures and exhibit a possibility to justify the key construction used in Gaifman's (...)
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  18.  29
    A Note on the Lambek-van Benthem Calculus.Wojciech Buszkowski - 1984 - Bulletin of the Section of Logic 13 (1):31-35.
    van Benthem [1] introduces a variant of Lambek Syntactic Calculus , proposed by Lambek [6], we call the variant Lambek-van Benthem Calculus . As proved by van Benthem, LBC is complete with respect to a semantics of λ-terms. In this note we indicate other relevant properties of LBC , just supporting some expectations of van Benthem. Given a countable set P r, of primitive types, the set T p, of types, is the smallest one such that: T p contains P (...)
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  19.  20
    Embedding Boolean Structures Into Atomic Boolean Structures.Wojciech Buszkowski - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (13-16):227-228.
  20.  19
    Logical Complexity of Some Classes of Tree Languages Generated by Multiple-Tree-Automata.Wojciech Buszkowski - 1980 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (1-6):41-49.
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  21.  18
    Representation Theorems for Implication Structures.Wojciech Buszkowski - 1996 - Bulletin of the Section of Logic 25:152-158.
  22.  8
    Concerning the Axioms of Ackermann's Set Theory.Wojciech Buszkowski - 1985 - Mathematical Logic Quarterly 31 (1‐6):63-70.
  23.  6
    Logical Complexity of Some Classes of Tree Languages Generated by Multiple‐Tree‐Automata.Wojciech Buszkowski - 1980 - Mathematical Logic Quarterly 26 (1‐6):41-49.
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  24.  3
    Embedding Boolean Structures Into Atomic Boolean Structures.Wojciech Buszkowski - 1986 - Mathematical Logic Quarterly 32 (13‐16):227-228.
  25.  2
    Incomplete Information Systems and Kleene 3-Valued Logic.Wojciech Buszkowski - 1997 - Poznan Studies in the Philosophy of the Sciences and the Humanities 57:201-220.
  26. Categorial Grammar.Wojciech Buszkowski, Witold Marciszewski & Johan van Benthem - 1991 - Studia Logica 50 (1):171-172.
     
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  27.  24
    Concerning the Axioms of Ackermann's Set Theory.Wojciech Buszkowski - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (1-6):63-70.
  28.  38
    Editorial Introduction.Wojciech Buszkowski & Michael Moortgat - 2002 - Studia Logica 71 (3):261-275.
  29.  35
    Editorial Introduction.Wojciech Buszkowski & Anne Preller - 2007 - Studia Logica 87 (2-3):139-144.
  30.  15
    Grammatical Structures and Logical Deductions.Wojciech Buszkowski - 1995 - Logic and Logical Philosophy 3:47-86.
    The three essays presented here concern natural connections between grammatical derivations and structures provided by certain standard grammar formalisms, on the one hand, and deductions in logical systems, on the other hand. In the first essay we analyse the adequacy of Polish notation for higher-order languages. The Ajdukiewicz algorithm (Ajdukiewicz 1935) is discussed in terms of generalized MP-deductions. We exhibit a failure in Ajdukiewicz’s original version of the algorithm and give a correct one; we prove that generalized MP-deductions have the (...)
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  31.  4
    On Families of Languages Generated by Categorial Grammar.Wojciech Buszkowski - 1998 - Poznan Studies in the Philosophy of the Sciences and the Humanities 62:39-48.
  32.  5
    On Involutive Nonassociative Lambek Calculus.Wojciech Buszkowski - 2019 - Journal of Logic, Language and Information 28 (2):157-181.
    Involutive Nonassociative Lambek Calculus is a nonassociative version of Noncommutative Multiplicative Linear Logic, but the multiplicative constants are not admitted. InNL adds two linear negations to Nonassociative Lambek Calculus ; it is a strongly conservative extension of NL Logical aspects of computational linguistics. LNCS, vol 10054. Springer, Berlin, pp 68–84, 2016). Here we also add unary modalities satisfying the residuation law and De Morgan laws. For the resulting logic InNLm, we define and study phase spaces. We use them to prove (...)
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  33. Relational Logics for Formalization of Database Dependencies.Wojciech Buszkowski & Ewa Orlowska - 1998 - Bulletin of the Section of Logic 27.
     
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  34.  20
    Strong Generative Capacity of Classical Categorial Grammars.Wojciech Buszkowski - 1986 - Bulletin of the Section of Logic 15 (2):60-63.
    Classical categorial grammars are the grammars introduced by Ajdukiewicz [1] and formalized by Bar-Hillel [2], Bar-Hillel et al. [3]. In [3] there is proved the weak equivalence of CCG’s and context-free grammars [6]. In this note we characterize the strong generative capacity of finite and rigid CCG’s, i.e. their capacity of structure generation. These results are more completely discussed in [4], [5].
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  35.  3
    The Ajdukiewicz Calculus, Polish Notation and Hilbert-Style Proofs.Wojciech Buszkowski - 1998 - In Katarzyna Kijania-Placek & Jan Woleński (eds.), The Lvov-Warsaw School and Contemporary Philosophy. Kluwer Academic Publishers. pp. 241--252.
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  36.  23
    Transition From Potential to Actual Infinity Via Ackermann's Principle.Wojciech Buszkowski - 1983 - Bulletin of the Section of Logic 12 (4):148-150.
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  37. Zasady gramatyki kategorialnej w świetle współczesnych formalizacji.Wojciech Buszkowski - 1988 - Studia Filozoficzne 271 (6-7).
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  38.  23
    Reviews. [REVIEW]Reinhold Kołodziej, Wojciech Buszkowski & Jan Waszkiewicz - 1976 - Studia Logica 35 (2):203-211.