Abstract Graph normal form, GNF, [1], was used in [2, 3] for analyzing paradoxes in propositional discourses, with the semantics—equivalent to the classical one—defined by kernels of digraphs. The paper presents infinitary, resolution-based reasoning with GNF theories, which is refutationally complete for the classical semantics. Used for direct (not refutational) deduction it is not explosive and allows to identify in an inconsistent discourse, a maximal consistent subdiscourse with its classical consequences. Semikernels, generalizing kernels, provide the semantic interpretation.

Finding the case id in unlabeled event logs is arguably one of the hardest challenges in process mining research. While this problem can be addressed with greedy approaches, these usually converge to sub-optimal solutions. In this paper, we describe an approach to perform complete search over the search space. We formulate the problem as a matter of finding the minimal set of patterns contained in a sequence, where patterns can be interleaved but do not have repeating symbols. We show that for practical purposes it is possible to reduce the search space to maximal disjoint occurrences of these patterns. Experimental results suggest that, whenever this approach finds a solution, it usually finds a minimal one.

We introduce a framework that generalizes algebraic specifications by equipping algebras with descriptions of evaluation strategies. The resulting abstract mathematical description allows one to model the implementation of algebras on various platforms in a way that is independent of the function-oriented specifications. We study algebras with associated data dependencies. The latter provide separate means for modelling computational aspects apart from the functional specifications captured by an algebra. The formalization of evaluation strategies (1) introduces increased portability among different hardware platforms, and (2) allows a potential increase in execution efficiency, since a chosen evaluation strategy may be tailored to a particular platform. We present the development process where algebraic specifications are equipped with data dependencies, the latter are refined, and, finally, mapped to actual hardware architectures.

The article defines algebraic semantics of singular (call-time-choice) and plural (run-time-choice) nondeterministic parameter passing and presents a specification language in which operations with both kinds of parameters can be defined simultaneously. Sound and complete calculi for both semantics are introduced. We study the relations between the two semantics and point out that axioms for operations with plural arguments may be considered as axiom schemata for operations with singular arguments.

The current algebraic models for nondeterminism focus on the notion of possibility rather than necessity and consequently equate (nondeterministic) terms that one would intuitively not consider equal. Furthermore, existing models for nondeterminism depart radically from the standard models for (equational) specifications of deterministic operators. One would prefer that a specification language for nondeterministic operators be based on an extension of the standard model concepts, preferably in such a way that the reasoning system for (possibly nondeterministic) operators becomes the standard equational one whenever restricted to the deterministic operators—the objective should be to minimize the departure from the standard frameworks. In this article we define a specification language for nondeterministic operators and multialgebraic semantics. The first complete reasoning system for such specifications is introduced. We also define a transformation of specifications of nondeterministic operators into derived specifications of deterministic ones, obtaining a “computational” semantics of nondeterministic specification by adopting the standard semantics of the derived specification as the semantics of the original one. This semantics turns out to be a refinement of multialgebra semantics. The calculus is shown to be sound and complete also with respect to the new semantics.