A deductive model checking approach for hybrid systems

In this paper we propose a verification method for hybrid systems that is based on a successive elimination of the various system locations involved. Briefly, with each such elimination we compute a weakest precondition (strongest postcondition) on the predecessor (successor) locations such that the property to be proved cannot be violated. This is done by representing a given verification problem as a second-order predicate logic formula which is to be solved (proved valid) with the help of a second-order quantifier elimination method. In contrast to many ``standard'' model checking approaches the method as described in this paper does not perform a forward or backward reachability analysis. Experiments show that this approach is particularly interesting in cases where a standard reachability analysis would require to travel often through some of the given system locations. In addition, the approach offers possibilities to proceed where ``standard'' reachability analysis approaches do not terminate

Motel user manual

MOTEL is a logic-based knowledge representation languages of the KL-ONE family. It contains as a kernel the KRIS language which is a decidable sublanguage of first-order predicate logic. Whereas KRIS is a single-agent knowledge representation system, i.e. KRIS is only able to represent general world knowledge or the knowledge of one agent about the world, MOTEL is a multi-agent knowledge representation system. The MOTEL language allows modal contexts and modal concept forming operators which allow to represent and reason about the believes and wishes of multiple agents. Furthermore it is possible to represent defaults and stereotypes. Beside the basic resoning facilities for consistency checking, classification, and realization, MOTEL provides an abductive inference mechanism. Furthermore it is able to give explanations for its inferences

SPASS-SATT: A CDCL(LA) Solver

International audienceSPASS-SATT is a CDCL(LA) solver for linear rational and linear mixed/integer arithmetic. This system description explains its specific features: fast cube tests for integer solvability, bounding transformations for unbounded problems, close interaction between the SAT solver and the theory solver, efficient data structures, and small-clause-normal-form generation. SPASS-SATT is currently one of the strongest systems on the respective SMT-LIB benchmarks

First-order modal logic theorem proving and standard PROLOG

Many attempts have been started to combine logic programming and modal logics. Most of them however, do not use classical PROLOG, but extend the PROLOG idea in order to cope with modal logic formulae directly. These approaches have the disadvantage that for each logic new logic programming systems are to be developed and the knowledge and experience gathered from PROLOG can hardly be utilized. Modal logics based on Kripke-style relational semantics, however, allow a direct translation from modal logic into first-order predicate logic by a straightforward translation of the given relational semantics. Unfortunately such a translation turns out to be rather na\"{\i}ve as the size of formulae increases exponentially during the translation. This paper now introduces a translation method which avoids such a representational overhead. Its basic idea relies on the fact that any binary relation can be replaced by equations and inequations which (under certain circumstances) can be eliminated later on by some further transformation. The overall approach thus works essentially for any modal logic having a Kripke-style possible world semantics and first-order describable frame properties. If at all, its application as a pre-processing for PROLOG is limited merely by the possibility of having frame properties which are not Horn or not even first-order describable

First‐order Modal Logic Theorem Proving and Functional Simulation

We propose a translation approach from modal logics to first‐order predicate \u000Alogic which combines advantages from both, the (standard) relational \u000Atranslation and the (rather compact) functional translation method and avoids \u000Amany of their respective disadvantages (exponential growth versus equality \u000Ahandling).\\ In particular in the application to serial modal logics it allows \u000Aconsiderable simplifications such that often even a simple unit clause suffices \u000Ain order to express the accessibility relation properties.\\ Although we \u000Arestrict the approach here to first‐order modal logic theorem proving it has \u000Abeen shown to be of wider interest, as e.g.~sorted logic or terminological \u000Alogic

Resolution-Based Calculi for Modal and Temporal Logics

In this paper a technique is presented which provides us with a means to develop resolution-based calculi for (first-order) modal and temporal logics. The approach is based on three parts: A special translation technique from modal and temporal logic formulae into classical predicate logic, a certain kind of saturation technique which is to be applied to given background theories, and an extraction of either suitable ``simpler'' background theories or logic-specific inference rules. The former is interesting in case existing classical logic theorem provers are to be utilized; the latter gains importance if one is prepared to extend theorem provers that are already at hand

Strong skolemization

Skolemization is a means to eliminate existential quantifiers within predicate logic sentences and that by replacing existentially quantified variables with Skolem function applications. The arguments of these Skolem functions are variables which are quantified outside the sub-formula under consideration. In this paper a Skolemization technique is introduced which abstracts from some of the arguments of the Skolem functions. It shows that the Skolemization result obtained this way is usually more general than what can be achieved from standard (classical) Skolemization. This can be of quite some importance since such generalizations often lead to a reduction of both search space and proof length

Modal Frame Characterization by Way of Auxiliary Modalities

In modal logics we are interested in classes of frames that characterize the logic under consideration. Such classes are usually distinguished by their respective frame properties. In general these characterizations are not unique and it is desirable to find a strongest possible. In this article an approach is presented which helps in this respect. It allows us to transform a given background theory into one which is more general and which modal logics cannot distinguish from the former because of their syntactic and semantic restrictions. The underlying technique is based on the idea to find conservative extensions of a given logic whose frame properties allow us to extract significantly stronger characterizations of the original logic