Labelled Tableaux for Distributed Temporal Logic

The distributed temporal logic DTL is a logic for reasoning about temporal properties of discrete distributed systems from the local point of view of the system's agents, which are assumed to execute sequentially and to interact by means of synchronous event sharing. We present a sound and complete labelled tableaux system for full DTL. To achieve this, we first formalize a labelled tableaux system for reasoning locally at each agent and afterwards we combine the local systems into a global one by adding rules that capture the distributed nature of DTL. We also provide examples illustrating the use of DTL and our tableaux syste

A History of Until

Until is a notoriously difficult temporal operator as it is both existential and universal at the same time: A until B holds at the current time instant w iff either B holds at w or there exists a time instant w' in the future at which B holds and such that A holds in all the time instants between the current one and w'. This "ambivalent" nature poses a significant challenge when attempting to give deduction rules for until. In this paper, in contrast, we make explicit this duality of until to provide well-behaved natural deduction rules for linear-time logics by introducing a new temporal operator that allows us to formalize the "history" of until, i.e., the "internal" universal quantification over the time instants between the current one and w'. This approach provides the basis for formalizing deduction systems for temporal logics endowed with the until operator. For concreteness, we give here a labeled natural deduction system for a linear-time logic endowed with the new operator and show that, via a proper translation, such a system is also sound and complete with respect to the linear temporal logic LTL with until.Comment: 24 pages, full version of paper at Methods for Modalities 2009 (M4M-6

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