Theoretical Computer Science
Automata-Theoretic techniques for modal logics of programs
Journal of Computer and System Sciences
Gentzen-type systems and resolution rules. Part I. Propositional logic
COLOG-88 Proceedings of the international conference on Computer logic
Attributive concept descriptions with complements
Artificial Intelligence
A guide to completeness and complexity for modal logics of knowledge and belief
Artificial Intelligence
Theoretical Computer Science
Reasoning about infinite computations
Information and Computation
The complexity of concept languages
Information and Computation
A class of decidable information logics
MFCS '96 Selected papers from the 21st symposium on Mathematical foundations of computer science
The nondeterministic information logic NIL is PSPACE-complete
Fundamenta Informaticae
On model checking for the &mgr;-calculus and its fragments
Theoretical Computer Science
Modal logic
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Incomplete Information: Structure, Inference, Complexity
Incomplete Information: Structure, Inference, Complexity
The complexity of propositional linear temporal logics in simple cases
Information and Computation
Single Step Tableaux for Modal Logics
Journal of Automated Reasoning
A Modal Logic for Data Analysis
MFCS '96 Proceedings of the 21st International Symposium on Mathematical Foundations of Computer Science
Reasoning about The Past with Two-Way Automata
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Emptiness Relations in Property Systems
ReIMICS '01 Revised Papers from the 6th International Conference and 1st Workshop of COST Action 274 TARSKI on Relational Methods in Computer Science
Proceedings of the Symposium on Logical Foundations of Computer Science: Logic at Botik '89
Presburger modal logic is PSPACE-Complete
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Hi-index | 5.23 |
The LA-logics ("logics with Local Agreement") are polymodal logics defined semantically such that at any world of a model, the sets of successors for the different accessibility relations can be linearly ordered and the accessibility relations are equivalence relations. In a previous work, we have shown that every LA-logic defined with a finite set of modal indices has an NP-complete satisfiability problem. In this paper, we introduce a class of LA-logics with a countably infinite set of modal indices and we show that the satisfiability problem is PSPACE-complete for every logic of such a class. The upper bound is shown by exhibiting a tree structure of the models. This allows us to establish a surprising correspondence between the modal depth of formulae and the number of occurrences of distinct modal connectives. More importantly, as a consequence, we can show the PSPACE-completeness of Gargov's logic DALLA and Nakamura's logic LGM restricted to modal indices that are rational numbers, for which the computational complexity characterization has been open until now. These logics are known to belong to the class of information logics and fuzzy modal logics, respectively.