Formalising deontic concepts, such as obligation, prohibition and permission, is normally carried out in a modal logic with a possible world semantics, in which some worlds are better than others. The main focus in these logics is on inferring logical consequences, for example inferring that the obligation O q is a logical consequence of the obligations O p and O. In this paper we propose a non-modal approach in which obligations are preferred ways of satisfying goals expressed in first-order logic. (...) To say that p is obligatory, but may be violated, resulting in a less than ideal situation s, means that the task is to satisfy the goal p ∨ s, and that models in which p is true are preferred to models in which s is true. Whereas, in modal logic, the preference relation between possible worlds is part of the semantics of the logic, in this non-modal approach, the preference relation between first-order models is external to the logic. Although our main focus is on satisfying goals, we also formulate a notion of logical consequence, which is comparable to the notion of logical consequence in modal deontic logic. In this formalisation, an obligation O p is a logical consequence of goals G, when p is true in all best models of G. We show how this non-modal approach to the treatment of deontic concepts deals with problems of contrary-to-duty obligations and normative conflicts, and argue that the approach is useful for many other applications, including abductive explanations, defeasible reasoning, combinatorial optimisation, and reactive systems of the production system variety. (shrink)

Logic programs under answer set semantics have become popular as a knowledge representation formalism in Artificial Intelligence. In this paper we investigate the possibility of using answer sets for qualitative decision making. Our approach is based on an extension of the formalism, called logic programs with ordered disjunction (LPODs). These programs contain a new connective called ordered disjunction. The new connective allows us to represent alternative, ranked options for problem solutions in the heads of rules: A × B intuitively means: (...) if possible A, but if A is not possible then at least B. The semantics of logic programs with ordered disjunction is based on a preference relation on answer sets. We show that LPODs can serve as a basis for qualitative decision making. (shrink)

The Independent Choice Logic , proposed by Poole, is a language for expressing probabilistic information in logic programming that adopts a distribution semantics: an ICL theory defines a distribution over a set of normal logic programs. The probability of a query is then given by the sum of the probabilities of the programs where the query is true. The ICL semantics requires the theory to be acyclic. This is a strong limitation that rules out many interesting programs. In this paper (...) we present an extension of the ICL semantics that allows theories to be modularly acyclic. Inference with ICL can be performed with the Ailog2 system that computes explanations to queries and then makes them mutually incompatible by means of an iterative algorithm. We propose the system PICL that computes the explanations to queries by means of a modification of SLDNF-resolution and then makes the explanations mutually incompatible by means of Binary Decision Diagrams. PICL and Ailog2 are compared on problems that involve computing the probability of a connection between two nodes in biological graphs and in social networks. Moreover, they are also applied to three games of dice. The problems considered are easily expressible in P-log, a probabilistic language based on Answer Set Programming. Therefore, the Plog system was also applied to the programs. PICL was able to handle larger problems than Ailog2 and Plog. Moreover, it was the fastest of the three algorithms except for one case of one of dice games. (shrink)