Related papers: Evaluation of Logic Programs with Built-Ins and Ag…
Basic arithmetic is the cornerstone of mathematics and computer sciences. In arithmetic, 'division by zero' is an undefined operation and any attempt at extending logic for algebraic division to incorporate division by zero has resulted in…
In a previous paper, a tableau calculus has been presented, which constitute a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work extends such a calculus to multi-modal…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
This article surveys recent advances in applying algebraic techniques to constraint satisfaction problems.
In the past years, analyzers have been introduced to detect classes of non-terminating queries for definite logic programs. Although these non-termination analyzers have shown to be rather precise, their applicability on real-life Prolog…
The possibility of translating logic programs into functional ones has long been a subject of investigation. Common to the many approaches is that the original logic program, in order to be translated, needs to be well-moded and this has…
The purpose of a program analysis is to compute an abstract meaning for a program which approximates its dynamic behaviour. A compositional program analysis accomplishes this task with a divide-and-conquer strategy: the meaning of a program…
Logical reasoning is essential in a variety of human activities. A representative example of a logical task is mathematics. Recent large-scale models trained on large datasets have been successful in various fields, but their reasoning…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…
We describe here a simple application of rational trees to the implementation of an interpreter for a procedural language written in a logic programming language. This is possible in languages designed to support rational trees (such as…
Effectivity functions are the basic formalism for investigating the semantics game logic. We discuss algebraic properties of stochastic effectivity functions, in particular the relationship to stochastic relations, morphisms and congruences…
We aim to reason about the correctness of behaviour-preserving transformations of Erlang programs. Behaviour preservation is characterised by semantic equivalence. Based upon our existing formal semantics for Core Erlang, we investigate…
The Curry-Howard correspondence is about a relationship between types and programs on the one hand and propositions and proofs on the other. The implications for programming language design and program verification is an active field of…
This is an extended survey of the results concerning a hierarchy of languages that is tightly connected with the quantifier alternation hierarchy within the two-variable fragment of first order logic of the linear order.
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
Moving from the mathematical theory of (abstract) syntax, we develop a general relational theory of symbolic manipulation parametric with respect to, and accounting for, general notions of syntax. We model syntax relying on categorical…
A foundation is investigated for the application of loosely structured data on the Web. This area is often referred to as Linked Data, due to the use of URIs in data to establish links. This work focuses on emerging W3C standards which…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
This paper presents a study of the metaphorism pattern of relational specification, showing how it can be refined into recursive programs. Metaphorisms express input-output relationships which preserve relevant information while at the same…