Joaquim Nunes Aparício

Non-monotonic reasoning with logic programming

Abstract Our purpose is to exhibit a modular systematic method of representing non-monotonic reasoning problems with the Well-Founded Semantics WFS of extended logic programs augmented with eXplicit negation (WFSX), augmented by its Contradiction Removal Semantics (CRSX) when needed. We apply this semantics, and its contradiction removal semantics counterpart, to represent non-monotonic reasoning problems. We show how to cast in the language of logic programs extended with explicit negation such forms of non-monotonic reasoning as defeasible reasoning, abductive reasoning, and hypothetical reasoning and apply them to such different domains of knowledge representation as hierarchies and reasoning about actions. We then abstract a modular systematic method of representing non-monotonic problems in a logic programming semantics comprising two forms of negation avoiding some drawbacks of other proposals, with which we relate our work.

Delta Prolog: A Distributed Backtracking Extension with Events

We present Delta Prolog, a distributed logic programming language that extends Prolog to include AND-parallelism (in a single processor or across a network of processors), interprocess communication via message passing with two-way pattern matching, interprocess synchronization with simultaneous message passing, and distributed backtracking among a family of processes. The extension is achieved, at the language level, by just two additional types of goals — events and splits. The implementation is written part in Prolog and part in C, with a small number of core primitives, to help portability. It is still experimental and expected to evolve. In this work we present the languages distinguishing features, describe its semantics, exhibit programs and analyse their behaviour, examine the implementation, and mention conclusions, advantages of the approach and the next developments.

Contradiction Removal Semantics with Explicit Negation

Well Founded Semantics for logic programs extended with eXplicit negation (WFSX) is characterized by the fact that, in any model, whenever ¬ia (the explicit negation of a) holds, then ∼ a (the negation by default of a) also holds.

Default Theory for Well Founded Semantics with Explicit Negation

One aim of this paper is to define a default theory for Well Founded Semantics of logic programs which have been extended with explicit negation, such that the models of a program correspond exactly to the extensions of the default theory corresponding to the program.

The Extended Stable Models of Contradiction Removal Semantics

Our purpose is to define a semantics that extends Contradiction Removal Semantics just as Extended Stable Model Semantics extends Well Founded Semantics, thus providing the notion of Contradiction Free Extended Stable Models. Contradiction Removal Semantics extends Well Founded Semantics to deal with contradictions arising from the introduction of classical negation. Because the Extended Stable Models structure of a program is useful for expressing defaults and abduction, it is important to study in what way the structure of the Extended Stable Models is affected by Contradiction Removal Semantics when the Well Founded Model is contradictory. Given that the Contradiction Removal Semantics is useful for expressing belief revision and counterfactual reasoning, dealing with the structure of such models is expected to be useful for mixing together all four mentioned kinds of reasoning within a single common framework.

Logic Programming for Non-Monotonic Reasoning

Our purpose is to develop a modular systematic method of representing nonmonotonic reasoning problems with the Well Founded Semantics of extended logic programs augmented with eXplicit negation (WFSX), and augmented by its Contradiction Removal Semantics (CRSX) when needed. We show how to cast in the language of such logic programs forms of non-monotonic reasoning like defeasible reasoning and hypothetical reasoning, and apply them to different domains of knowledge representation, for instance taxonomic hierarchies and reasoning about actions. We then abstract a modular systematic method of representing non-monotonic problems in logic programming.

Expressing Population Based Optimization Heuristics Using PLATO

There are presently many and seemingly different optimization algorithms, based on unrelated paradigms. Although some nice and important intuitions support those heuristics, there is (to our knowledge) no rigorous and systematic approach on how to relate them. Herein we present a framework to encompass those heuristics, based on the multiset formalism, providing a common working structure and a basis for their comparison. We show how to express some well known heuristics in our framework and we present some results on relations among them.

Assumption Set Semantics (The Procedures)

Our purpose is to extend logic programming semantics for programs with some form of denial statements [2] specifying that some sets of literals cannot all belong to the meaning of a program. Denials represent an intuitive form of knowledge representation extending the capabilities of logic programming as a tool for knowledge representation and reasoning. In [2] we defined the intended meaning of a program with a set of denials, and show that a set of denials is isomorphic to sets of assumption based denials. The model theory we introduce there is clearly general in the sense it does not rely on any particular semantics. A consequence is that satisfaction of (denials) may be seen as satisfaction w.r.t. to a smaller class of models (revised models) which are also stable under a suitable operator. Operationally, satisfaction of denials is equivalent to membership of the set of assumption based denials, thus avoiding the need for general consistency checking, which are more suitable (in some sense) for logic programming based implementations.