This paper presents a syntax of approximate formulae suited for the logic with counting quantifiers SOLP. This logic was formalised by us in [1] where, among other properties, we showed the following facts: (i) In the presence of a built–in (linear) order, SOLP can describe NP–complete problems and some of its fragments capture the classes P and NL; (ii) weakening the ordering relation to an al...

The second and revised edition of this little book has now made its appearance. It is as the authors state intended for medical students, a class difficult to cater for as regards chemistry. At the present date the medical curriculum is as much as the student can assimilate and the demand on the specialist teacher to present his subject in a short and concise way is not easy. This book designed...

In this paper we address ground logics, a family of nonmonotonic modal logics, and their usage in knowledge representation. In such a setting non-modal sentences are used to represent the knowledge of an agent about the world, while an epistemic operator provides the agent with autoepistemic or introspective knowledge. Ground logics are based on the idea of characterizing the knowledge of the a...

Craig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic. A few of these results non-trivially generalize known interpolation results; all the others are new. We also discuss some applications of our results to the theory of institutio...

The basic logic programming semantic concepts, query, solutions, solution forms, and the fundamental results such as Herbrand theorems, are developed over any logical system, formalised as institution, by employing ‘institution-independent’ concepts of variable, substitution, quantifier, and atomic formulae. This sets semantical foundations for an uniform development of logic programming over a...

In this paper, the exact formulae for the generalized degree distance, degree distance and reciprocal degree distance of strong product of a connected and the complete multipartite graph with partite sets of sizes m0, m1, . . . , mr&minus1 are obtained. Using the results obtained here, the formulae for the degree distance and reciprocal degree distance of the closed and open fence graphs are co...

The need for integration of classical logic with nonmonotonic rules has been gaining importance in areas like the Semantic Web and Open Multi-Agent Systems. A number of researchers addressed this problem by proposing a unified semantics for knowledge bases composed of both first-order formulae and rules (also called hybrid knowledge bases). These semantics have matured over the years, but only ...

We present SAM, a symbolic model checker for ACTL, the action-based version of CTL. SAM relies on implicit representations of Labeled Transition Systems (LTSs), the semantic domain for ACTL for-mulae, and uses symbolic manipulation algorithms. SAM has been realized by translating (networks of) LTSs and, possibly recursive, ACTL formulae into BSP (Boolean Symbolic Programming), a programming lan...

We establish that the quantifier alternation hierarchy of formulae of secondorder propositional modal logic (SOPML) induces an infinite corresponding semantic hierarchy over the class of finite directed graphs. This solves an open problem problem of van Benthem (1985) and ten Cate (2006). We also identify modal characterizations of the expressive powers of second-order logic (SO) and monadic se...