Monodic temporal logic with quantified propositional variables

We extend the monodic fragment of first-order linear temporal logic to include right-linear grammar operators and quantification of propositional variables. Unlike propositional temporal logic, the use of grammar operators in first-order temporal logic is not equivalent to general propositional quantification, as the latter admit satisfiable formulae without countable models. We consider the decision problem for fragments where propositional quantification occurs outside of quantification of individual variables and temporal (grammar) operators. We show that if externally quantified propositions inside temporal operators occur within positive occurrences of universal quantifiers for individual variables, then validity for all propositional prefix classes is recursively enumerable and decidable in the two-variable case. Without this condition we show that, even with very severe restrictions on the first-order part of the logic, no non-trivial prefix class is recursively enumerable

On non-local propositional and weak monodic quantified CTL

Accepted versio

Complexity of monodic guarded fragments over linear and real time

Accepted versio

Automated Analysis of Compositional Multi-Agent Systems

Abstract. An approach for handling the complex dynamics of a multi-agent system is based on distinguishing aggregation levels. The behaviour at a given aggregation level is specified by a set of dynamic properties at that level, expressed in some (temporal) language. Such behavioural specifications may be complex and difficult to analyse. To enable automated analysis of system specifications, a simpler format is required. To this end, a specification at a lower aggregation level can be created, describing basic steps in the processes of a system. This paper presents a method and tool to support the automated creation of such a specification, as a refinement of a given higher level specification. The generated specification has a simple format which can easily be used for analysis. This paper describes an approach for automated verification of logical consequences of specifications using model checking techniques

Counterpart semantics for a second-order mu-calculus

We propose a novel approach to the semantics of quantified μ-calculi, considering models where states are algebras; the evolution relation is given by a counterpart relation (a family of partial homomorphisms), allowing for the creation, deletion, and merging of components; and formulas are interpreted over sets of state assignments (families of substitutions, associating formula variables to state components). Our proposal avoids the limitations of existing approaches, usually enforcing restrictions of the evolution relation: the resulting semantics is a streamlined and intuitively appealing one, yet it is general enough to cover most of the alternative proposals we are aware of

Interactions between Knowledge and Time in a First-Order Logic for Multi-Agent Systems: Completeness Results

We investigate a class of first-order temporal-epistemic logics for reasoning about multiagent systems. We encode typical properties of systems including perfect recall, synchronicity, no learning, and having a unique initial state in terms of variants of quantified interpreted systems, a first-order extension of interpreted systems. We identify several monodic fragments of first-order temporal-epistemic logic and show their completeness with respect to their corresponding classes of quantified interpreted systems. 1

Combining Spatial and Temporal Logics: Expressiveness vs. Complexity

In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PTL, the spatial logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and computational realisability within the hierarchy. We demonstrate how different combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out of components that are at most NP- or PSPACE-complete