Alexander Bolotov

Natural deduction calculus for linear-time temporal logic

We present a natural deduction calculus for the propositional linear-time temporal logic and prove its correctness. The system extends the natural deduction construction of the classical propositional logic. This will open the prospect to apply our technique as an automatic reasoning tool in a deliberative decision making framework across various AI applications.

A resolution method for CTL branching-time temporal logic

We extend our clausal resolution method for linear temporal logics to a branching-time framework. The branching-time temporal logics considered are computation tree logic (CTL), often regarded as the simplest useful logic of this class, and extended CTL (ECTL), which is CTL extended with fairness operators. The key elements of the resolution method, namely the normal form, the concept of step resolution and a novel temporal resolution rule, are introduced and justified with respect to both these logics. A completeness argument is provided, together with an example of the use of the temporal resolution method. Finally, we consider future work, in particular extension of the method yet further, to CTL*, and implementation of the approach by utilising techniques developed for linear-time temporal resolution.

Clausal resolution in a logic of rational agency

A resolution based proof system for a Temporal Logic of Possible Belief is presented. This logic is the combination of the branching-time temporal logic CTL (representing change over time) with the modal logic KD45 (representing belief). Such combinations of temporal or dynamic logics and modal logics are useful for specifying complex properties of multi-agent systems. Proof methods are important for developing verification techniques for these complex multi-modal logics. Soundness, completeness and termination of the proof method are shown and simple examples illustrating its use are given.

Natural Deduction Calculus for Computation Tree Logic

The authors present a natural deduction calculus for the computation tree logic, CTL, defined with the full set of classical and temporal logic operators. The system extends the natural deduction construction of the linear-time temporal logic. This opens the prospect to apply our technique as an automatic reasoning tool in a deliberative decision making framework across various applications in AI and computer science, where the branching-time setting is required

Automated Natural Deduction for Propositional Linear-Time Temporal Logic

We present a proof searching technique for the natural deduction calculus for the prepositional linear-time temporal logic and prove its correctness. This opens the prospect to apply our technique as an automated reasoning tool in a number of emerging computer science applications and in a deliberative decision making framework across various AI applications.

Towards gcm re-configuration - extending specification by norms

We continue investigation of formal specification of Grid Component systems by temporal logics and subsequent application of temporal resolution as a verification technique. This time we enrich the specification language by the ability to capture norms which enables us to formally define a concept of a re-configuration. We aim at integrating a software tool for automated specification as well as verification to ensure a reliable and dynamically re-configurable model.

A clausal resolution method for branching-time logic ECTL+

We expand the applicability of the clausal resolution technique to the branching-time temporal logic ECTL+. ECTL+ is strictly more expressive than the basic computation tree logic CTL and its extension, ECTL, as it allows Boolean combinations of fairness and single temporal operators. We show how any ECTL+ formula can be translated to a normal form the structure of which was initially defined for CTL and then used for ECTL. This enables us to apply to ECTL+ a resolution technique defined over the set of clauses. Both correctness of the method and complexity of the transformation procedure are given.

Clausal Resolution for CTL

In this paper we consider proof techniques for branching-time temporal logics. While a considerable amount of research heis been carried out regarding the relationship between finite automata and such logics, practical proof techniques for such logics have received relatively little attention. Recently, however, several applications requiring refined proof methods for branching-time temporal logics have appeared, most notably the specification and verification of multi-agent systems. Thus, here we extend our clausal resolution method for linear-time temporal logics to a branching-time framework, in particular to the powerful CTL* logic. The key elements of the resolution method, namely the normal form, the concept of step resolution and a novel temporal resolution rule, Eire introduced, justified, and applied.

Search strategies for resolution in CTL-type logics: extension and complexity

A clausal resolution approach originally developed for the branching logic CTL has recently been extended to the logics ECTL and ECTL/sup +/. In the application of the resolution rules searching for a loop is essential. In this paper, we define a depth-first technique to complement the existing breadth-first search and provide the complexity analysis of the developed methods. Additionally, it contains a correction in our previous presentation of loops.

A clausal resolution method for extended computation tree logic ECTL

A temporal clausal resolution method was originally developed for linear time temporal logic and further extended to the branching-time framework of Computation Tree Logic (CTL). In this paper, following our general idea to expand the applicability of this efficient method to more expressive formalisms useful in a variety of applications in computer science and AI requiring branching time logics, we define a clausal resolution technique for Extended Computation Tree Logic (ECTL). The branching-time temporal logic ECTL is strictly more expressive than CTL, in allowing fairness operators. The key elements of the resolution method for ECTL, namely the clausal normal form, the concepts of step resolution and a temporal resolution, are introduced and justified with respect to this new framework. Although in developing these components we incorporate many of the techniques defined for CTL, we need novel mechanisms in order to capture fairness together with the limit closure property of the underlying tree models. We accompany our presentation of the relevant techniques by examples of the application of the temporal resolution method. Finally, we provide a correctness argument and consider future work discussing an extension of the method yet further, to the logic CTL, the most powerful logic of this class.