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Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…

Separation Logic is an effective Program Logic for proving programs that involve pointers. Reasoning with pointers becomes difficult especially when there is aliasing arising due to several pointers to a given cell location. In this paper,…

Fixpoint operators are tools to reason on recursive programs and data types obtained by induction (e.g. lists, trees) or coinduction (e.g. streams). They were given a categorical treatment with the notion of categories with fixpoints. A…

Logic programming with tabling and constraints (TCLP, tabled constraint logic programming) has been shown to be more expressive and, in some cases, more efficient than LP, CLP, or LP with tabling. In this paper we provide insights regarding…

An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…

Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of…

In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…

This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…

Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, i.e.\ operators whose range are sets…

On one hand, termination analysis of logic programs is now a fairly established research topic within the logic programming community. On the other hand, non-termination analysis seems to remain a much less attractive subject. If we divide…

The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms whose logical values cannot be inferred from the rules. Thus, the well founded semantics corresponds to the…

We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general term-orderings (instead of level mappings), like it is done in transformational approaches to logic program…

Termination is an important and well-studied property for logic programs. However, almost all approaches for automated termination analysis focus on definite logic programs, whereas real-world Prolog programs typically use the cut operator.…

We provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the…

Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates…

Logical reasoning about program data often requires dealing with heap structures as well as scalar data types. Recent advances in Satisfiability Modular Theory (SMT) already offer efficient procedures for dealing with scalars, yet they lack…

The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…

This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for…

This paper describes a general framework for automatic termination analysis of logic programs, where we understand by ``termination'' the finitenes s of the LD-tree constructed for the program and a given query. A general property of…

We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the…