ion in Fixpoint Logic SJOERD CRANEN, MACIEJ GAZDA, WIEGER WESSELINK and TIM A.C. WILLEMSE, Eindhoven University of Technology We present a theory of abstraction for the framework of parameterised Boolean equation systems, a firstorder fixpoint logic. Parameterised Boolean equation systems can be used to solve a variety of problems in verification. We study the capabilities of the abstraction th...

Linear rules have played an increasing role in structural proof theory in recent years. It has been observed that the set of all sound linear inference rules in Boolean logic is already coNP-complete, i.e. that every Boolean tautology can be written as a (leftand right-)linear rewrite rule. In this paper we study properties of systems consisting only of linear inferences. Our main result is tha...

By a strong conceptual completeness (XC) statement for a logical doctrine we mean an assertion that says that any theory of the doctrine can be recovered from an appropriate structure formed by the models of the theory. The expression ‘logical doctrine’ is used here as in [9] to mean a specific selection of logical operations giving rise to a notion of theory, in the form of a structured catego...

At present, the filter theory of $BL$textit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor $BL$textit{-}algebras. Note that fil...

This thesis presents NC(T ), an extension of the DPLL(T ) scheme [16, 29] for decision procedures for quantifier-free first-order logics. In DPLL(T ), a general Boolean DPLL engine is instantiated with a theory solver for the theory T . The DPLL engine is responsible for computing Boolean implications and detecting Boolean conflicts, while the theory solver detects implications and conflicts in...

Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may, however, introduce dynamical possibilities that are not accessible to the original system. We show that large random networks of variables coupled through con...