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Wojciech Zielonka [18]Wojciech P. Zielonka [2]
  1.  23
    Axiomatizability of Ajdukiewicz-Lambek Calculus by Means of Cancellation Schemes.Wojciech Zielonka - 1981 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 27 (13-14):215-224.
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  2.  23
    A Direct Proof of the Equivalence of Free Categorial Grammars and Simple Phrase Structure Grammars.Wojciech Zielonka - 1978 - Studia Logica 37 (1):41 - 57.
    In [2], Bar-Hillel, Gaifman, and Shamir prove that the simple phrase structure grammars (SPGs) defined by Chomsky are equivalent in a certain sense to Bar-Hillel's bidirectional categorial grammars (BCGs). On the other hand, Cohen [3] proves the equivalence of the latter ones to what the calls free categorial grammars (FCGs). They are closely related to Lambek's syntactic calculus which, in turn, is based on the idea due to Ajdukiewicz [1]. For the reasons which will be discussed in the last section, (...)
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  3.  11
    Axiomatizability of Ajdukiewicz‐Lambek Calculus by Means of Cancellation Schemes.Wojciech Zielonka - 1981 - Mathematical Logic Quarterly 27 (13‐14):215-224.
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  4.  27
    Interdefinability of Lambekian Functors.Wojciech Zielonka & W. Zielonka - 1992 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):501-507.
  5.  55
    A Simple and General Method of Solving the Finite Axiomatizability Problems for Lambek's Syntactic Calculi.Wojciech Zielonka - 1989 - Studia Logica 48 (1):35 - 39.
    In [4], I proved that the product-free fragment L of Lambek's syntactic calculus (cf. Lambek [2]) is not finitely axiomatizable if the only rule of inference admitted is Lambek's cut-rule. The proof (which is rather complicated and roundabout) was subsequently adapted by Kandulski [1] to the non-associative variant NL of L (cf. Lambek [3]). It turns out, however, that there exists an extremely simple method of non-finite-axiomatizability proofs which works uniformly for different subsystems of L (in particular, for NL). We (...)
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  6.  61
    Cut-Rule Axiomatization of the Syntactic Calculus NL.Wojciech Zielonka - 2000 - Journal of Logic, Language and Information 9 (3):339-352.
    An axiomatics of the product-free syntactic calculus L ofLambek has been presented whose only rule is the cut rule. It was alsoproved that there is no finite axiomatics of that kind. The proofs weresubsequently simplified. Analogous results for the nonassociativevariant NL of L were obtained by Kandulski. InLambek's original version of the calculus, sequent antecedents arerequired to be nonempty. By removing this restriction, we obtain theextensions L 0 and NL 0 ofL and NL, respectively. Later, the finiteaxiomatization problem for L (...)
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  7.  24
    Cut-Rule Axiomatization of Product-Free Lambek Calculus With the Empty String.Wojciech Zielonka - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (2):135-142.
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  8.  16
    Interdefinability of Lambekian Functors.Wojciech Zielonka & W. Zielonka - 1992 - Mathematical Logic Quarterly 38 (1):501-507.
    Several Gentzen-style syntactic type calculi with product are considered. They form a hierarchy in such a way that one calculus results from another by imposing a new condition upon the sequent-forming operation. It turns out that, at some steps of this process, two different functors collapse to a single one. For the remaining stages of the hierarchy, analogues of Wajsbergs's theorem on non-mutual-definability are proved.
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  9.  13
    Cut‐Rule Axiomatization of Product‐Free Lambek Calculus With the Empty String.Wojciech Zielonka - 1988 - Mathematical Logic Quarterly 34 (2):135-142.
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  10.  21
    Cut-Rule Axiomatization of the Syntactic Calculus L.Wojciech Zielonka - 2001 - Journal of Logic, Language and Information 10 (2):339-352.
    In Zielonka (1981a, 1989), I found an axiomatics for the product-free calculus L of Lambek whose only rule is the cut rule. Following Buszkowski (1987), we shall call such an axiomatics linear. It was proved that there is no finite axiomatics of that kind. In Lambek's original version of the calculus (cf. Lambek, 1958), sequent antecedents are non empty. By dropping this restriction, we obtain the variant L 0 of L. This modification, introduced in the early 1980s (see, e.g., Buszkowski, (...)
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  11.  10
    On Reduction Systems Equivalent to the Lambek Calculus with the Empty String.Wojciech Zielonka - 2002 - Studia Logica 71 (1):31-46.
    The paper continues a series of results on cut-rule axiomatizability of the Lambek calculus. It provides a complete solution of a problem which was solved partially in one of the author''s earlier papers. It is proved that the product-free Lambek Calculus with the empty string (L 0) is not finitely axiomatizable if the only rule of inference admitted is Lambek''s cut rule. The proof makes use of the (infinitely) cut-rule axiomatized calculus C designed by the author exactly for this purpose.
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  12.  24
    Linear Axiomatics of Commutative Product-Free Lambek Calculus.Wojciech Zielonka - 1990 - Studia Logica 49 (4):515 - 522.
    Axiomatics which do not employ rules of inference other than the cut rule are given for commutative product-free Lambek calculus in two variants: with and without the empty string. Unlike the former variant, the latter one turns out not to be finitely axiomatizable in that way.
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  13.  19
    On the Equivalence of Ajdukiewicz-Lambek Calculus and Simple Phrase Structure Grammars.Wojciech Zielonka - 1976 - Bulletin of the Section of Logic 5 (2):1-4.
    In [2], Bar-Hillel, Gaifman, and Shamir prove that the simple phrase structure grammars dened by Chomsky are equivalent in a cer- tain sense to Bar-Hillel's bidirectional categorial grammars . On the other hand, Cohen [3] proves the equivalence of the latter ones to what he calls free categorial grammars . They are closely related to Lambek's syntactic calculus which is, in turn, based on the idea due to Ajdukiewicz [1]. For some reasons, Cohen's proof seems to be at least in- (...)
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  14.  19
    JM Cohen's Claim on Categorial Grammars Remains Unproved.Wojciech Zielonka - 1985 - Bulletin of the Section of Logic 14 (4):130-133.
    Joel M. Cohen , pp. 475- 484) claims that Lambek’s categorial grammars are equivalent in a certain natural sense to those of Bar-Hillel, Gaifman, and Shamir. Unfortunately, it turns out that Cohen’s proof is based on a false lemma. Thus the equivalence of both kinds of grammars is still an open problem although there is much evidence in its favor. This paper yields a counterexample to Cohen’s lemma.
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  15.  27
    Reviews. [REVIEW]Wojciech P. Zielonka & Jerzy Kopania - 1975 - Studia Logica 34 (4):387-399.
  16.  15
    Two Weak Lambek-Style Calculi: DNL and DNL.Wojciech Zielonka - 2012 - Logic and Logical Philosophy 21 (1):53-64.
    The calculus DNL results from the non-associative Lambek calculus NL by splitting the product functor into the right (⊲) and left (⊳) product interacting respectively with the right (/) and left () residuation. Unlike NL, sequent antecedents in the Gentzen-style axiomatics of DNL are not phrase structures (i.e., bracketed strings) but functor-argument structures. DNL − is a weaker variant of DNL restricted to fa-structures of order ≤ 1. When axiomatized by means of introduction/elimination rules for / and , it shows (...)
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  17.  4
    More About the Axiomatics of the Lambek Calculus.Wojciech Zielonka - 1997 - Poznan Studies in the Philosophy of the Sciences and the Humanities 57:319-326.