A tableau-like proof procedure for normal modal logics

AbstractIn this paper a new proof procedure for some propositional and first-order normal modal logics is given. It combines a tableau-like approach and a resolution-like inference. Completeness and decidability for some propositional logics are proved. An extension for the first-order case is presented

Open architectures for formal reasoning and deductive technologies for software development

The objective of this project is to develop an open architecture for formal reasoning systems. One goal is to provide a framework with a clear semantic basis for specification and instantiation of generic components; construction of complex systems by interconnecting components; and for making incremental improvements and tailoring to specific applications. Another goal is to develop methods for specifying component interfaces and interactions to facilitate use of existing and newly built systems as 'off the shelf' components, thus helping bridge the gap between producers and consumers of reasoning systems. In this report we summarize results in several areas: our data base of reasoning systems; a theory of binding structures; a theory of components of open systems; a framework for specifying components of open reasoning system; and an analysis of the integration of rewriting and linear arithmetic modules in Boyer-Moore using the above framework

Tactic-based theorem proving in first-order modal and temporal logics

We describe the ongoing work on a tactic-based theorem prover for First-Order Modal and Temporal Logics (FOTLs for the temporal ones). In formal methods, especially temporal logics play a determining role; in particular, FOTLs are natural whenever the modeled systems are in nite-state. But reasoning in FOTLs is hard and few approaches have so far proved eective. Here we introduce a family of sequent calculi for rst-order modal and temporal logics which is modular in the structure of time; moreover, we present a tactic-based modal/temporal theorem prover enforcing this approach, obtained employing the higher-order logic programming language Prolog. Finally, we show some promising experimental results and raise some open issues. We believe that, together with the Proof Planning approach, our system will eventually be able to improve the state of the art of formal methods through the use of FOTLs.

Dynamic Logic with Trace Semantics

Dynamic logic is an established instrument for program verification and for reasoning about the semantics of programs and programming languages. In this paper, we define an extension of dynamic logic, called Dynamic Trace Logic (DTL), which combines the expressiveness of program logics such as dynamic logic with that of temporal logic. And we present a sound and relatively complete sequent calculus for proving validity of DTL formulae. Due to its expressiveness, DTL can serve as a basis for proving functional and information-flow properties in concurrent programs, among other applications

Resolution Proof Technique in Linear Temporal Logic.

This dissertation presents a resolution proof technique for Propositional Linear Temporal Logic of discrete time with the Until operator. The presented proof technique stems from the resolution method developed by L. Farinas del Cerro and A. Cavalli. However, their method is incomplete, and their completeness proof, as originally reported, is incorrect. Unlike Farinas\u27s method, our proof technique incorporated the Until operator, which is a very powerful and useful in describing complex temporal relationships which are common in many areas of computer science. Our technique is also proved complete. The presented resolution method for linear temporal logic is similar to classical resolutions: the main goal is to show unsatisfiability of a set of temporal clauses by locating, either directly or indirectly, a state which contains unsatisfiability. Subsequent resolvents of a refutation are obtained by resolving out complementary literals referring to the same instant of time. In order to increase the efficiency of the resolution proof technique, we have developed a refinement of the presented basic method. This refinement is similar to the well-known Ordered Linear (OL) strategy for classical resolution. We also present the lifting of the basic resolution method to predicate linear temporal logic. Unlike First Order Logic, clauses of predicate linear temporal logic may contain variables which are quantified existentially, because skolemization is not valid here. We use standard unification with substitution on universally quantified variables. However, if a term substituted in place of a variable contains any flexible symbols, a constant or a function is flexible if it has different translation in different states, then all occurrences of the substituted variable must refer to the same instant of time (state). Otherwise, the unification may lead to incorrect results. Resolution in predicate linear temporal logic, though very useful from a practical standpoint, is incomplete, since no predicate temporal logic with arithmetic model of time is complete