Infinitary Action Logic with Exponentiation

  title={Infinitary Action Logic with Exponentiation},
  author={Stepan L. Kuznetsov and Stanislav O. Speranski},
  journal={Ann. Pure Appl. Log.},
4 Citations

Commutative Action Logic

We prove undecidability and pinpoint the place in the arithmetical hierarchy for commutative action logic, that is, the equational theory of commutative residuated Kleene lattices (action lattices),

Relational Models for the Lambek Calculus with Intersection and Constants

. We consider relational semantics (R-models) for the Lambek calculus extended with intersection and explicit constants for zero and unit. For its variant without constants and a restriction which



Subexponentials in non-commutative linear logic

Conditions for when cut elimination is admissible in the presence of non-commutative subexponentials are investigated, investigating the interaction of the exchange rule with the local and non-local contraction rules.

On Action Logic: Equational Theories of Action Algebras

It is shown that Jipsen’s system for action logic does not admit cut-elimination, and it is proved that the equational theory of *-continuous action algebras and the simple Horn theory of -continuous Kleene alge Bras are not recursively enumerable and they possess FMP, but action logicdoes not possess F MP.

Algorithmic specifications in linear logic with subexponentials

This work shows that focused proof search can be precisely linked to a simple algorithmic specification language that contains while-loops, conditionals, and insertion into and deletion from multisets and proposes a new logical connective that allows for the creation of new subexponentials, thereby further augmenting the algorithmic expressiveness of logic.

The Complexity of Multiplicative-Additive Lambek Calculus: 25 Years Later

It is proved, in contrast with the polynomial-time result for the product-free Lambek calculus with one implication, that the derivability problem is still PSPACE-complete even for a very small fragment, including one implication and conjunction only.

On the complexity of reasoning in Kleene algebra

  • D. Kozen
  • Mathematics, Computer Science
    Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science
  • 1997
We study the complexity of reasoning in Kleene algebra and *-continuous Kleene algebra in the presence of extra equational assumptions E; that is, the complexity of deciding the validity of universal

Higher recursion theory

Hyperarithmetic theory is the first step beyond classical recursion theory. It is the primary source of ideas and examples in higher recursion theory. It is also a crossroad for several areas of

Reconciling Lambek's restriction, cut-elimination, and substitution in the presence of exponential modalities

It is shown that for any system equipped with a reasonable exponential modality the following holds: if the system enjoys cut elimination and substitution to the full extent, then the system necessarily violates Lambek's restriction, and two of the three conditions can be implemented.

Substructural Operational Semantics as Ordered Logic Programming

The substructural framework thereby provides a new methodology for language specification that synthesizes structural operational semantics, abstract machines, and logical approaches.

The Logic of Categorial Grammars: A deductive account of natural language syntax and semantics

This book shows how categorial grammars weave together converging ideas from formal linguistics, typed lambda calculus, Montague semantics, proof theory and 1 linear logic, thus yielding a coherent and formally elegant framework for natural language syntax and semantics.

Lambek calculus is NP-complete