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

We develop a conceptually clear, intuitive, and feasible decision procedure for testing satisfiability in the full multi-agent epistemic logic CMAEL(CD) with operators for common and distributed knowledge for all coalitions of agents mentioned in the language. To that end, we introduce Hintikka structures for CMAEL(CD) and prove that satisfiability in such structures is equivalent to satisfiability in standard models. Using that result, we design an incremental tableau-building procedure that eventually constructs a satisfying Hintikka structure for every satisfiable input set of formulae of CMAEL(CD) and closes for every unsatisfiable input set of formulae.Comment: Substantially extended and corrected version of arXiv:0902.2125. To appear in: Logic Journal of the IGPL, special issue on Formal Aspects of Multi-Agent System

Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables

We show that Branching-time temporal logics CTL and CTL*, as well as Alternating-time temporal logics ATL and ATL*, are as semantically expressive in the language with a single propositional variable as they are in the full language, i.e., with an unlimited supply of propositional variables. It follows that satisfiability for CTL, as well as for ATL, with a single variable is EXPTIME-complete, while satisfiability for CTL*, as well as for ATL*, with a single variable is 2EXPTIME-complete,--i.e., for these logics, the satisfiability for formulas with only one variable is as hard as satisfiability for arbitrary formulas.Comment: Prefinal version of the published pape

Reducing Validity in Epistemic ATL to Validity in Epistemic CTL

We propose a validity preserving translation from a subset of epistemic Alternating-time Temporal Logic (ATL) to epistemic Computation Tree Logic (CTL). The considered subset of epistemic ATL is known to have the finite model property and decidable model-checking. This entails the decidability of validity but the implied algorithm is unfeasible. Reducing the validity problem to that in a corresponding system of CTL makes the techniques for automated deduction for that logic available for the handling of the apparently more complex system of ATL.Comment: In Proceedings SR 2013, arXiv:1303.007

A Faster Tableau for CTL*

There have been several recent suggestions for tableau systems for deciding satisfiability in the practically important branching time temporal logic known as CTL*. In this paper we present a streamlined and more traditional tableau approach built upon the author's earlier theoretical work. Soundness and completeness results are proved. A prototype implementation demonstrates the significantly improved performance of the new approach on a range of test formulas. We also see that it compares favourably to state of the art, game and automata based decision procedures.Comment: In Proceedings GandALF 2013, arXiv:1307.416

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

Automated Synthesis of Tableau Calculi

This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filtration with respect to a well-defined first-order semantics then adding a general blocking mechanism provides a terminating tableau calculus. The process of generating tableau rules can be completely automated and produces, together with the blocking mechanism, an automated procedure for generating tableau decision procedures. For illustration we show the workability of the approach for a description logic with transitive roles and propositional intuitionistic logic.Comment: 32 page

Strategic logics : complexity, completeness and expressivity

by transferring normative attributes from an agent to another. Such interactions are called delegation. Formal models of delegation and control were studied in, e.g., [189, 149, 191]. In this work, we consider the scenario where agents delegate control over propositions to other agents. The distinction between controllable and uncontrollable propositions stems from areas like discrete event systems and control theory, where, e.g., Boutilier [39] studied control in the context of deontic logic. Control and controllable propositions were also studied in [52, 66, 249, 248]. We now give an overview of the thesis. The main purpose of Chapter 2 is to introduce basic concepts and notation and to review relevant literature. The first section presents a brief survey on modal logic. Then, in sections 2.2, 2.3 and 2.4, we introduce epistemic, temporal and strategic modal logics and state known results that characterise their expressivity and computational complexity. In particular, we consider variants of ATL as extensions of branching-time logics. With such ATL-like logics we can describe dynamic multi-agent interactions. In Section 2.5, we discuss extensions of ATL with epistemic notions. Additionally, we suggest a framework for memory-bounded strategic reasoning. In particular, we introduce an epistemic variant of ATL that accounts for agents with limited memory resources as this case was neglected in the literature to date. In Chapter 3, we investigate the computational complexity of ATL and its epistemic extension ATEL. We show in detail how 'the complexity of the satisfiability problem for both logics can be settled at ExpTIME-complete. The part of the chapter about ATL is based on the paper 'ATL Satisfiability is Indeed ExpTIME-COmplete' by Walther, Lutz, Wolter and Wooldridge in the Journal of Logic and Computation, 2006 (265)' and the part about ATEL is based on the paper 'ATEL with Common and Distributed Knowledge is ExpTime-Complete' by Walther which was presented at the 4th Workshop on Methods for Modalities, Humbolt University, Berlin, December 1-2, 2005 [264]. In Chapter 4, we aim to extend the expressiveness of ATL without increasing its computational complexity. We introduce explicit names for strategies in the object language and extend modal operators with the possibility to bind agents to strategy names. In this way, we can fix the decisions of agents that possibly belong to several coalitions. By identifying the behaviqur of agents, we can reason about the effects of agents changing coalitions. Dynamic coalitions provide more flexibility to adapt abilities to a changing environment. We investigate the expressivity of the resulting logic ATLES and compare it to ATL and ATL*. Moreover, we formulate two model checking problems for ATLES and investigate their complexity as well as the complexity of the satisfiability problem for ATLES. Additionally, we present a complete axiomatisation. This chapter is based on the paper 'Alternating-time Temporal Logic with Explicit Strategies' by Walther, van der Hoek and Wooldridge which is going to presented at the 11th Conference on Theoretical Aspects of Rationality and Knowledge (TARK), Brussels, Belgium, June 25-27, 2007 [266]