Correction to: Preface

EPiC Series in Computing

We analyze the space complexity of monitoring streams of messages whose expected behavior is specified in a fragment of predicate logic; this fragment is the core of the LogicGuard specification language that has been developed in industrial context for the runtime monitoring of network traffic. The execution of the monitors is defined by an operational semantics for the step-wise evaluation of formulas, of which require the preservation of instances of the formulas in memory until their truth value can be determined. In the presented work, we analyze the number of instances that have to be preserved over time for a significant fragment of the core language that involves only “future looking quantifiers” which lays the foundations for the space analysis of the entire core language.

2005

Theorema is a project that aims at supporting the entire process of mathematical theory exploration within one coherent logic and software system. This survey paper illustrates the style of Theorema-supported mathematical theory exploration by a case study (the automated synthesis of an algorithm for the construction of Gröbner Bases) and gives an overview on some reasoners and organizational tools for theory exploration developed in the Theorema project.

Lecture Notes in Computer Science, 2022

Anti-unification aims at computing generalizations for given terms, retaining their common structure and abstracting differences by variables. We study quantitative anti-unification where the notion of the common structure is relaxed into "proximal" up to the given degree with respect to the given fuzzy proximity relation. Proximal symbols may have different names and arities. We develop a generic set of rules for computing minimal complete sets of approximate generalizations and study their properties. Depending on the characterizations of proximities between symbols and the desired forms of solutions, these rules give rise to different versions of concrete algorithms.

Proceedings of UNIF, 2005

Abstract. We describe a matching algorithm for terms built over flexible arity function symbols and context, function, sequence, and individual variables. The algorithm is called a context sequence matching algorithm. Context variables allow matching to descend in term-trees ...

… of the 18th International Workshop on …, 2004

We study term equations with sequence variables and sequence function symbols. A sequence variable can be instantiated by any finite sequence of terms, including the empty sequence. A sequence function abbreviates a finite sequence of functions all having the ...

2016

PρLog extends Prolog by conditional transformations that are controlled by strategies. We give a brief overview of the tool and illustrate its capabilities. 1998 ACM Subject Classification D.1.6 Logic Programming, F.4.2 Grammars and Other Rewriting Systems, D.3.2 Language Classifications

2021

Anti-unification aims at computing generalizations for given terms, retaining their common structure and abstracting differences by variables. We study anti-unification for full fuzzy signatures, where the notion of common structure is relaxed into a "proximal" one with respect to a given proximity relation. Mismatches between both symbol names and their arities are permitted. We develop algorithms for different cases of the problem and study their properties.

Pattern matching with membership constraints for hedge and context variables is a desirable capability for the analysis and decomposition of structures that can be presented as hedges in an algebra with flexible arity function symbols. We distinguish two kinds of patterns: for hedges and for contexts, i.e., sequences of terms with one or more occurrences of a placeholder for a nonempty hedge. Our patterns are a generalization of regular expressions where, besides regular operators we also employ hedge variables and context variables whose admissible bindings are subjected to membership constraints. We propose a matching algorithm that is sound and complete under some reasonable restrictions on the structure of the matching problem.

Journal of Formalized Reasoning, 2016

The Theorema project aims at the development of a computer assistant for the working mathematician. Support should be given throughout all phases of mathematical activity, from introducing new mathematical concepts by definitions or axioms, through first (computational) experiments, the formulation of theorems, their justification by an exact proof, the application of a theorem as an algorithm, to the dissemination of the results in form of a mathematical publication, the build up of bigger libraries of certified mathematical content and the like. This ambitious project is exactly along the lines of the QED manifesto issued in 1994 (see e.g. http://www.cs.ru.nl/~freek/qed/qed.html) and it was initiated in the mid-1990s by Bruno Buchberger. The Theorema system is a computer implementation of the ideas behind the Theorema project. One focus lies on the natural style of system input (in form of definitions, theorems, algorithms, etc.), system output (mainly in form of mathematical proofs) and user interaction. Another focus is theory exploration, i.e. the development of large consistent mathematical theories in a formal frame, in contrast to just proving single isolated theorems. When using the Theorema system, a user should not have to follow a certain style of mathematics enforced by the system (e.g. basing all of mathematics on set theory or certain variants of type theory), rather should the system support the user in her preferred flavor of doing math. The new implementation of the system, which we refer to as Theorema 2.0, is open-source and available through GitHub.

Lecture Notes in Computer Science

In this paper we define an unranked nominal language, an extension of the nominal language with tuple variables and term tuples. We define the unification problem for unranked nominal terms and present an algorithm solving the unranked nominal unification problem.