Refinement Modal Logic

In this paper we present {\em refinement modal logic}. A refinement is like a bisimulation, except that from the three relational requirements only `atoms' and `back' need to be satisfied. Our logic contains a new operator 'all' in addition to the standard modalities 'box' for each agent. The operator 'all' acts as a quantifier over the set of all refinements of a given model. As a variation on a bisimulation quantifier, this refinement operator or refinement quantifier 'all' can be seen as quantifying over a variable not occurring in the formula bound by it. The logic combines the simplicity of multi-agent modal logic with some powers of monadic second-order quantification. We present a sound and complete axiomatization of multi-agent refinement modal logic. We also present an extension of the logic to the modal mu-calculus, and an axiomatization for the single-agent version of this logic. Examples and applications are also discussed: to software verification and design (the set of agents can also be seen as a set of actions), and to dynamic epistemic logic. We further give detailed results on the complexity of satisfiability, and on succinctness

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

Automata games for multiple-model checking

3-valued models have been advocated as a means of system abstraction such that verifications and refutations of temporal-logic properties transfer from abstract models to the systems they represent. Some application domains, however, require multiple models of a concrete or virtual system. We build the mathematical foundations for 3-valued property verification and refutation applied to sets of common concretizations of finitely many models. We show that validity checking for the modal mu-calculus has the same cost (EXPTIME-complete) on such sets as on all 2-valued models, provide an efficient algorithm for checking whether common concretizations exist for a fixed number of models, and propose using parity games on variants of tree automata to efficiently approximate validity checks of multiple models. We prove that the universal topological model in [M. Huth, R. Jagadeesan, and D. A. Schmidt. A domain equation for refinement of partial systems. Mathematical Structures in Computer Science, 14(4):469-505, 5 August 2004] is not bounded complete. This confirms that the approximations aforementioned are reasonably precise only for tree-automata-like models, unless all models are assumed to be deterministic. © 2006 Elsevier B.V. All rights reserved

Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm

On the complexity of semantic self-minimization

Partial Kripke structures model only parts of a state space and so enable aggressive abstraction of systems prior to verifying them with respect to a formula of temporal logic. This partiality of models means that verifications may reply with true (all refinements satisfy the formula under check), false (no refinement satisfies the formula under check) or dont know. Generalized model checking is the most precise verification for such models (all dont know answers imply that some refinements satisfy the formula, some dont), but computationally expensive. A compositional model-checking algorithm for partial Kripke structures is efficient, sound (all answers true and false are truthful), but may lose precision by answering dont know instead of a factual true or false. Recent work has shown that such a loss of precision does not occur for this compositional algorithm for most practically relevant patterns of temporal logic formulas. Formulas that never lose precision in this manner are called semantically self-minimizing. In this paper we provide a systematic study of the complexity of deciding whether a formula of propositional logic, propositional modal logic or the propositional modal mu-calculus is semantically self-minimizing. © 2009 Elsevier B.V. All rights reserved

Partial Behavioural Models for Requirements and Early Design

The talk will discuss the problem of creation, management, and specifically merging of partial behavioural models, expressed as model transition systems. We argue why this formalism is essential in the early stages of the software cycle and then discuss why and how to merge information coming from different sources using this formalism. The talk is based on papers presented in FSE\u2704 and FME\u2706 and will also include emerging results on synthesizing partial behavioural models from temporal properties and scenarios

Labelled transition systems as a Stone space

A fully abstract and universal domain model for modal transition systems and refinement is shown to be a maximal-points space model for the bisimulation quotient of labelled transition systems over a finite set of events. In this domain model we prove that this quotient is a Stone space whose compact, zero-dimensional, and ultra-metrizable Hausdorff topology measures the degree of bisimilarity such that image-finite labelled transition systems are dense. Using this compactness we show that the set of labelled transition systems that refine a modal transition system, its ''set of implementations'', is compact and derive a compactness theorem for Hennessy-Milner logic on such implementation sets. These results extend to systems that also have partially specified state propositions, unify existing denotational, operational, and metric semantics on partial processes, render robust consistency measures for modal transition systems, and yield an abstract interpretation of compact sets of labelled transition systems as Scott-closed sets of modal transition systems.Comment: Changes since v2: Metadata updat