Proceedings ArticleDOI
The Logic of Action Lattices is Undecidable
Stepan L. Kuznetsov
- pp 1-9
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Algorithmic undecidability of the (in)equational theory of residuated Kleene lattices (action lattices) is proved, thus solving a problem left open by D. Kozen, P. Jipsen, W. Buszkowski.Abstract:
We prove algorithmic undecidability of the (in)equational theory of residuated Kleene lattices (action lattices), thus solving a problem left open by D. Kozen, P. Jipsen, W. Buszkowski.read more
Citations
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Journal ArticleDOI
Action Logic is Undecidable
TL;DR: This article proves that undecidability of action logic is undecidable, more precisely, for all recursively enumerable logics between action logic and infinitary action logic, for fragments of these logics with only one of the two lattice (additive) connectives, and for action logic extended with the law of distributivity.
Book ChapterDOI
Iterative Division in the Distributive Full Non-associative Lambek Calculus
TL;DR: In this article, an extension of the Distributive Full Non-associative Lambek Calculus with iterative division operators is studied, where the iterative operators can be seen as representing iterative composition of linguistic resources or of actions.
Journal ArticleDOI
The Multiplicative-Additive Lambek Calculus with Subexponential and Bracket Modalities
Max I. Kanovich,Max I. Kanovich,Stepan L. Kuznetsov,Stepan L. Kuznetsov,Andre Scedrov,Andre Scedrov +5 more
TL;DR: A proof-theoretic and algorithmic complexity analysis for systems introduced by Morrill to serve as the core of the CatLog categorial grammar parser shows that categorial grammars based on them can generate arbitrary recursively enumerable languages.
Journal ArticleDOI
A Restricted Fragment of the Lambek Calculus with Iteration and Intersection Operations
TL;DR: The Lambek calculus with intersection and iteration (Kleene star) was studied in this article, where it was shown that it is completeness both w.r.t.
Book ChapterDOI
Complexity of Commutative Infinitary Action Logic
TL;DR: In this paper, the authors considered commutative infinitary action logic and showed that its derivability problem is (varPi ∆ + 1/0)-complete for non-commutative *-continuous action lattices.
References
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Book
Introduction to the Theory of Computation
TL;DR: Throughout the book, Sipser builds students' knowledge of conceptual tools used in computer science, the aesthetic sense they need to create elegant systems, and the ability to think through problems on their own.
Book ChapterDOI
Representation of Events in Nerve Nets and Finite Automata
TL;DR: This memorandum is devoted to an elementary exposition of the problems and of results obtained on the McCulloch-Pitts nerve net during investigations in August 1951.
Journal ArticleDOI
The Mathematics of Sentence Structure
TL;DR: An effective rule (or algorithm) for distinguishing sentences from nonsentences is obtained, which works not only for the formal languages of interest to the mathematical logician, but also for natural languages such as English, or at least for fragments of such languages.
Journal ArticleDOI
A completeness theorem for Kleene algebras and the algebra of regular events
TL;DR: A finitary axiomatization of the algebra of regular events involving only equations and equational implications that is sound for all interpretations over Kleene algebras is given.