## 4 Citations

### Commutative Action Logic

- Mathematics
- 2021

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

- MathematicsArXiv
- 2022

. 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…

### A $\varPi _1^0$-Bounded Fragment of Infinitary Action Logic with Exponential

- MathematicsLogic, Language, and Security
- 2020

## References

SHOWING 1-10 OF 53 REFERENCES

### Subexponentials in non-commutative linear logic

- MathematicsMathematical Structures in Computer Science
- 2018

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

- MathematicsJ. Log. Comput.
- 2007

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

- Mathematics, Computer SciencePPDP '09
- 2009

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

- Computer Science, MathematicsWoLLIC
- 2019

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

- Mathematics, Computer ScienceProceedings 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

- Mathematics
- 1990

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

- MathematicsJ. Log. Comput.
- 2020

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

- Computer Science2009 24th Annual IEEE Symposium on Logic In Computer Science
- 2009

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

- Computer Science
- 2012

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.