Type Logics and Pregroups
نویسنده
چکیده
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
منابع مشابه
Wojciech Buszkowski Type Logics and Pregroups
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 (quasi-ordered) bilinear algebras and pregroups w...
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We consider finitely generated pregroups, and describe how an appropriately defined rewrite relation over words from a generating alphabet yields a natural partial order for a pregroup structure. We investigate the identity problem for pregroups; that is, the algorithmic determination of whether a word rewrites to the identity element. This problem is undecidable in general, however, we give a ...
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We study mathematical and algorithmic properties of Lambek’s pregroups and illustrate them by the French noun phrase. An algorithm of complexity 3 n to solve the reduction problem in an arbitrary free pregroup as well as recognition by a pregroup grammar is presented. This algorithm is then specified to run in linear time. A sufficient condition for a language fragment that makes the linear alg...
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ورودعنوان ژورنال:
- Studia Logica
دوره 87 شماره
صفحات -
تاریخ انتشار 2007