Dmitry Shkatov

Tableau-based decision procedures for logics of strategic ability in multiagent systems

We develop an incremental tableau-based decision procedure for the alternating-time temporal logic ATL and some of its variants. While running within the theoretically established complexity upper bound, we believe that our tableaux are 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.

Tableau Tool for Testing Satisfiability in LTL: Implementation and Experimental Analysis

We report on the implementation and experimental analysis of an incremental multi-pass tableau-based procedure a la Wolper for testing satisfiability in the linear time temporal logic LTL, based on a breadth-first search strategy. We describe the implementation and discuss the performance of the tool on several series of pattern formulae, as well as on some random test sets, and compare its performance with an implementation of Schwendimanns one-pass tableaux by Widmann and Gore on several representative series of pattern formulae, including eventualities and safety patterns. Our experiments have established that Schwendimanns algorithm consistently, and sometimes dramatically, outperforms the incremental tableaux, despite the fact that the theoretical worst-case upper-bound of Schwendimanns algorithm, 2EXPTIME, is worse than that of Wolpers algorithm, which is EXPTIME. This shows, once again, that theoretically established worst-case complexity results do not always reflect truly the practical efficiency, at least when comparing decision procedures.

Finding uniform strategies for multi-agent systems

We present an algorithm for finding uniform strategies in multi-agent systems with incomplete information. The algorithm finds all maximal uniform strategies for agents with incomplete information for enforcing a property expressible in the language of Alternating-time Temporal Logic ATL. The main application of the algorithm is automated program synthesis for systems that can be modeled as multi-agent systems with incomplete information (e.g., decentralized distributed systems).

Tableau-Based Procedure for Deciding Satisfiability in the Full Coalitional Multiagent Epistemic Logic

We study the multiagent epistemic logic CMAEL(CD) with operators for common and distributed knowledge for all coalitions of agents. We introduce Hintikka structures for this logic and prove that satisfiability in such structures is equivalent to satisfiability in standard models. Using this result, we design an incremental tableau based decision procedure for testing satisfiability in CMAEL(CD).

Tableau-Based Decision Procedure for the Multi-agent Epistemic Logic with Operators of Common and Distributed Knowledge

We develop an incremental-tableau-based decision procedure for the multi-agent epistemic logic MAEL(CD) (aka S5n (CD)), whose language contains operators of individual knowledge for a finite set Sigma agents of agents, as well as operators of distributed and common knowledge among all agents in agents. Our tableau procedure works in (deterministic) exponential time, thus establishing an upper bound for MAEL(cd)-satisfiability that matches the (implicit) lower-bound known from earlier results, which implies ExpTime-completeness of MAEL(CD)-satisfiability. Therefore, our procedure provides a complexity-optimal algorithm for checking MAEL(CD)-satisfiability, which, however, in most cases is much more efficient. We prove soundness and completeness of the procedure, and illustrate it with an example.

A general method for proving decidability of intuitionistic modal logics

Abstract We generalise the result of [H. Ganzinger, C. Meyer, M. Veanes, The two-variable guarded fragment with transitive relations, in: Proc. 14th IEEE Symposium on Logic in Computer Science, IEEE Computer Society Press, 1999, pp. 24–34] on decidability of the two variable monadic guarded fragment of first order logic with constraints on the guard relations expressible in monadic second order logic. In [H. Ganzinger, C. Meyer, M. Veanes, The two-variable guarded fragment with transitive relations, in: Proc. 14th IEEE Symposium on Logic in Computer Science, IEEE Computer Society Press, 1999, pp. 24–34], such constraints apply to one relation at a time. We modify their proof to obtain decidability for constraints involving several relations. Now we can use this result to prove decidability of multi-modal modal logics where conditions on accessibility relations involve more than one relation. Our main application is intuitionistic modal logic, where the intuitionistic and modal accessibility relations usually interact in a non-trivial way.

Complexity and expressivity of propositional dynamic logics with finitely many variables

We investigate the complexity of satisfiability for finite-variable fragments of propositional dynamic logics. We consider three formalisms belonging to three representative complexity classes, broadly understood,---regular PDL, which is EXPTIME-complete, PDL with intersection, which is 2EXPTIME-complete, and PDL with parallel composition, which is undecidable. We show that, for each of these logics, the complexity of satisfiability remains unchanged even if we only allow as inputs formulas built solely out of propositional constants, i.e. without propositional variables. Moreover, we show that this is a consequence of the richness of the expressive power of variable-free fragments: for all the logics we consider, such fragments are as semantically expressive as entire logics. We conjecture that this is representative of PDL-style, as well as closely related, logics.

Tableau-based decision procedure for the multiagent epistemic logic with all coalitional operators for common and distributed knowledge

We develop a conceptually clear, intuitive, and feasible de- cision procedure for testing satisability in the full multiagent epistemic logic CMAEL(CD) with operators for common and distributed knowl- edge for all coalitions of agents mentioned in the language. To that end, we introduce Hintikka structures for CMAEL(CD) and prove that sat- isability in such structures is equivalent to satisability in standard models. Using that result, we design an incremental tableau-building procedure that eventually constructs a satisfying Hintikka structure for every satisable input set of formulae of CMAEL(CD) and closes for every unsatisable input set of formulae.

Undecidability of First-Order Modal and Intuitionistic Logics with Two Variables and One Monadic Predicate Letter

We prove that the positive fragment of first-order intuitionistic logic in the language with two individual variables and a single monadic predicate letter, without functional symbols, constants, and equality, is undecidable. This holds true regardless of whether we consider semantics with expanding or constant domains. We then generalise this result to intervals