We consider the temporal language with the Priorean operators G and H expressing that a formula is true at all future times and all past times, plus an operator 2 expressing that a formula is true throughout some open interval containing the evaluation time (i.e., it is true ‘around now’). We show that the logic of time based on the real numbers in this language is finitely axiomatisable, answe...

We present Prioni, a tool that integrates model checking and theorem proving for relational reasoning. Prioni takes as input formulas written in Alloy, a declarative language based on relations. Prioni uses the Alloy Analyzer to check the validity of Alloy formulas for a given scope that bounds the universe of discourse. The Alloy Analyzer can refute a formula if a counterexample exists within ...

Quantifier Elimination We work in K a large rich differentially closed field. All other differential fields are assumed to be small subfields of K. Let L = {+,−, ·, δ, 0, 1} be the language of differential rings. We let L− = {+,−, ·, 0, 1}, the language of rings. If k is a differential field, we can view k either as an L-structure or an L−-structure. Theorem 1.1 (Quantifier Elimination) For any...

The use of bundle gerbes and bundle gerbe modules is considered as a replacement for the usual theory of Clifford modules on manifolds that fail to be spin. It is shown that both sides of the Atiyah-Singer index formula for coupled Dirac operators can be given natural interpretations using this language and that the resulting formula is still an identity.

The aim of this paper is counting the probability that a random modal formula is a tautology. We examine {→, 2} fragment of two modal logics S5 and S4 over the language with one propositional variable. Any modal formula written in such a language may be interpreted as a unary binary tree. As it is known, there are finitely many different formulas written in one variable in the logic S5 and this...

A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the language by a tree automaton with a fixed number of states, and expressing the mentioned requirements in a SAT formula. Satisfiability of this formula implies...

Monadic-second order logic (mso-logic) is successfully applied in both language theory and algorithm design. In the former, properties definable by mso-formulas are exactly the regular properties on many structures like, most prominently, strings. In the latter, solving a problem for structures of bounded tree width is routinely done by defining it in terms of an mso-formula and applying genera...

We considers how a particular kind of graph corresponds to multiplicative intuitionistic linear logic formula. The main feature of the graphical notation is that it absorbs certain symmetries between conjunction and implication. We look at the basic definitions and present details of an implementation in the functional programming language Standard ML. This provides a functional approach to gra...

A problem from thermodynamic formalism for countable symbolic Markov chains is considered. It concerns asymptotic behavior of the equilibrium measures corresponding to increasing sequences finite submatrices an infinite nonnegative matrix A <mm...