91 research outputs found
And-or tableaux for fixpoint logics with converse: LTL, CTL, PDL and CPDL
Over the last forty years, computer scientists have invented or borrowed numerous logics for reasoning about digital systems. Here, I would like to concentrate on three of them: Linear Time Temporal Logic (LTL), branching time Computation Tree temporal Logic (CTL), and Propositional Dynamic Logic (PDL), with and without converse. More specifically, I would like to present results and techniques on how to solve the satisfiability problem in these logics, with global assumptions, using the tableau method. The issues that arise are the typical tensions between computational complexity, practicality and scalability. This is joint work with Linh Anh Nguyen, Pietro Abate, Linda Postniece, Florian Widmann and Jimmy Thomson
From Display to Labelled Proofs for Tense Logics
We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt
Reasoning with global assumptions in arithmetic modal logics
We establish a generic upper bound ExpTime for reasoning with global assumptions in coalgebraic modal logics. Unlike earlier results of this kind, we do not require a tractable set of tableau rules for the in- stance logics, so that the result applies to wider classes of logics. Examples are Presburger modal logic, which extends graded modal logic with linear inequalities over numbers of successors, and probabilistic modal logic with polynomial inequalities over probabilities. We establish the theoretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that offers potential for practical reasoning
Tableau-based decision procedures for logics of strategic ability in multi-agent systems
We develop an incremental tableau-based decision procedures for the
Alternating-time temporal logic ATL and some of its variants.
While running within the theoretically established complexity upper bound, we
claim that our tableau is practically more efficient in the average case than
other decision procedures for ATL known so far. Besides, the ease of its
adaptation to variants of ATL demonstrates the flexibility of the proposed
procedure.Comment: To appear in ACM Transactions on Computational Logic. 48 page
Relating Sequent Calculi for Bi-intuitionistic Propositional Logic
Bi-intuitionistic logic is the conservative extension of intuitionistic logic
with a connective dual to implication. It is sometimes presented as a symmetric
constructive subsystem of classical logic.
In this paper, we compare three sequent calculi for bi-intuitionistic
propositional logic: (1) a basic standard-style sequent calculus that restricts
the premises of implication-right and exclusion-left inferences to be
single-conclusion resp. single-assumption and is incomplete without the cut
rule, (2) the calculus with nested sequents by Gore et al., where a complete
class of cuts is encapsulated into special "unnest" rules and (3) a cut-free
labelled sequent calculus derived from the Kripke semantics of the logic. We
show that these calculi can be translated into each other and discuss the
ineliminable cuts of the standard-style sequent calculus.Comment: In Proceedings CL&C 2010, arXiv:1101.520
A Non-wellfounded, Labelled Proof System for Propositional Dynamic Logic
We define a infinitary labelled sequent calculus for PDL, G3PDL^{\infty}. A
finitarily representable cyclic system, G3PDL^{\omega}, is then given. We show
that both are sound and complete with respect to standard models of PDL and,
further, that G3PDL^{\infty} is cut-free complete. We additionally investigate
proof-search strategies in the cyclic system for the fragment of PDL without
tests
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