Deciding ATL∗ Satisfiability by Tableaux Technical report

Optimal Tableaux-Based Decision Procedure for Testing Satisfiability in the Alternating-Time Temporal Logic ATL+

We develop a sound, complete and practically implementable tableaux-based decision method for constructive satisfiability testing and model synthesis in the fragment ATL of the full Alternating time temporal logic ATL∗. The method extends in an essential way a previously developed tableaux-based decision method for ATL and works in 2EXPTIME, which is the optimal worst case complexity of the sat...

Optimal Tableaux Method for Constructive Satisfiability Testing and Model Synthesis in the Alternating-time Temoral Logic ATL+

From ATL Tableaux to Alternating Automata

The logic called ATL (Alternating-time Temporal Logic) was introduced, in 1997, as a modal logic of agents. The first direct algorithm to test whether a given ATL-formula θ is satisfiable was provided by V. Goranko and G. van Drimmelen in 2006. Their algorithm is based on alternating infinite tree automata. In 2009, V. Goranko and D. Shkatov proposed a method to test satisfiability of a formula...

Satisfiability of Alternating-Time Temporal Epistemic Logic Through Tableaux

In this paper we present a tableau-based method to decide the satisfiability of formulas in ATEL, an extension of the alternating-time temporal logic ATL including epistemic modalities for individual knowledge. Specifically, we analyse satisfiability of ATEL formulas under a number of conditions. We evaluate the assumptions of synchronicity and of a unique initial state, which have been propose...

A traditional tree-style tableau for LTL

Propositional linear time temporal logic (LTL) is the standard temporal logic for computing applications and many reasoning techniques and tools have been developed for it. Tableaux for deciding satisfiability have existed since the 1980s. However, the tableaux for this logic do not look like traditional tree-shaped tableau systems and their processing is often quite complicated. We present a n...