Nested logic programs with ordered disjunction

In this paper we define a class of nested logic programs, nested logic programs with ordered disjunction (LPODs+), which allows to specify qualitative preferences by means of nested preference expressions. For doing this we extend the syntax of logic programs with ordered disjunction (LPODs) to capture more general expressions. We define the LPODs+ semantics in a simple way and we extend most of the results of logic programs with ordered disjunction showing how our approach effectively is a proper generalisation of LPODs.Peer ReviewedPostprint (published version

A preference meta-model for logic programs with possibilistic ordered disjunction

This paper presents an approach for specifying user preferences related to services by means of a preference meta-model, which is mapped to logic programs with possibilistic ordered disjunction following a Model-Driven Methodology (MDM). MDM allows to specify problem domains by means of meta-models which can be converted to instance models or other meta-models through transformation functions. In particular we propose a preference meta-model that defines an abstract preference specification language allowing users to specify preferences in a more friendly way using models. We also present a meta-model for logic programs with possibilistic order disjunction. Then we show how we conceptually map the preference meta-model to logic programs with possibilistic ordered disjunction by means of a mapping function.Peer ReviewedPostprint (published version

Towards the implementation of a preference-and uncertain-aware solver using answer set programming

Logic programs with possibilistic ordered disjunction (or LPPODs) are a recently defined logic-programming framework based on logic programs with ordered disjunction and possibilistic logic. The framework inherits the properties of such formalisms and merging them, it supports a reasoning which is nonmonotonic, preference-and uncertain-aware. The LPPODs syntax allows to specify 1) preferences in a qualitative way, and 2) necessity values about the certainty of program clauses. As a result at semantic level, preferences and necessity values can be used to specify an order among program solutions. This class of program therefore fits well in the representation of decision problems where a best option has to be chosen taking into account both preferences and necessity measures about information. In this paper we study the computation and the complexity of the LPPODs semantics and we describe the algorithm for its implementation following on Answer Set Programming approach. We describe some decision scenarios where the solver can be used to choose the best solutions by checking whether an outcome is possibilistically preferred over another considering preferences and uncertainty at the same time.Postprint (published version

Logic programs with possibilistic ordered disjunction

Logic programs with ordered disjunction have shown to be a flexible specification language able to model common user preferences in a natural way. However, in some realistic scenarios the preferences should be linked to the evidence of the information when trying to reach a single preferred solution. In this paper, we extend the syntax and the semantics of logic programs with ordered disjunction in order to cope with uncertain information. In particular, we define a possibilistic semantics for capturing possibilistic ordered disjunction programs. We use a simple example to explain the approach and outline an application scenario showing the benefits of possibilistic ordered disjunction.Postprint (published version

Logic programs with ordered disjunction: First-order semantics and expressiveness

Logic programs with ordered disjunction (LPODs) (Brewka 2002) generalize normal logic programs by combining alternative and ranked options in the heads of rules. It has been showed that LPODs are useful in a number of areas including game theory, policy languages, planning and argumentations. In this paper, we extend propositional LPODs to the first-order case, where a classical second-order formula is defined to capture the stable model semantics of the underlying first-order LPODs. We then develop a progression semantics that is equivalent to the stable model semantics but naturally represents the reasoning procedure of LPODs. We show that on finite structures, every LPOD can be translated to a firstorder sentence, which provides a basis for computing stable models of LPODs. We further study the complexity and expressiveness of LPODs and prove that almost positive LPODs precisely capture first-order normal logic programs, which indicates that ordered disjunction itself and constraints are sufficient to represent negation as failure.NPRP grant (NPRP 09-079-1-013) from the Qatar National Research Fund (QNRF).Scopu

A Novel Approach to the Semantics of Qualitative Choice Logic

Η Λογική Ποιοτικών Επιλογών (Qualitative Choice Logic, QCL), είναι μία επέκταση της κλασικής προτασιακής λογικής που μας επιτρέπει να εκφράσουμε τυπικά προτιμήσεις. Προσθέτει ένα νέο προτασιακό σύνδεσμο × που εκφράζει τη διατεταγμένη διάζευξη. Η διατεταγμένη διάζευξη των a και b, που εκφράζεται ως a × b, ικανοποιείται από το a ή το b, αλλά δηλώνει επιπλέον ότι προτιμάμε το a από το b. Ερμηνεύουμε διαισθητικά το a × b ως: «προτιμούμε το a αν είναι δυνατό, διαφορετικά ικανοποιούμαστε τουλάχιστον με το b». Τα Λογικά Προγράμματα με Διατεταγμένη Διάζευξη (Logic Programs with Ordered Disjunction, LPODs) είναι μία επέκταση των λογικών προγραμμάτων όπου οι κεφαλές των κανόνων αποτελούνται από διατεταγμένες διαζεύξεις. Στο [1], προτάθηκε μία νέα τετράτιμη μοντελοθεωρητική σημασιολογία για αυτά τα Λογικά Προγράμματα. Εμείς περιγράφουμε μία επέκταση της σημασιολογίας για τη Λογική Ποιοτικών Επιλογών και εξετάζουμε κάποια από τα προβλήματά της. Έπειτα, περιγράφουμε μία νέα απειρότιμη μοντελοθεωρητική σημασιολογία για πεπερασμένα σύνολα τύπων της Λογικής Ποιοτικών Επιλογών και παραθέτουμε ιδέες για το πώς θα μπορούσε να επεκταθεί και σε άπειρα σύνολα.Qualitative Choice Logic (QCL) is an extension of classical propositional logic that allows the expression of preferences in a formal way. It adds a new connective ×, which represents ordered disjunction. The ordered disjunction of a and b, expressed as a × b, is satisfied by a or b, but also denotes that the satisfaction of a is preferred to b. We intuitively interpret a × b as: “if possible, we prefer a, if not, then at least b”. Logic Programs with Ordered Disjunction (LPODs) are an extension of logic programs where the heads of rules are comprised of οrdered disjunctions. In [1], a new four-valued model-theoretic semantics for LPODs was introduced. We describe a natural extension of this semantics for QCL and examine some of its issues. We then describe a new infinite-value model-theoretic semantics for finite sets of QCL formulae and discuss how it could be extended to infinite sets as well

Characterizing and Extending Answer Set Semantics using Possibility Theory

Answer Set Programming (ASP) is a popular framework for modeling combinatorial problems. However, ASP cannot easily be used for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP. In PASP a weight is associated with each rule, where this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold. As such, it allows us to model and reason about uncertain information in an intuitive way. In this paper we present new semantics for PASP, in which rules are interpreted as constraints on possibility distributions. Special models of these constraints are then identified as possibilistic answer sets. In addition, since ASP is a special case of PASP in which all the rules are entirely certain, we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction, called weak disjunction, that has not been previously considered in the literature. In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity. In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.Comment: 39 pages and 16 pages appendix with proofs. This article has been accepted for publication in Theory and Practice of Logic Programming, Copyright Cambridge University Pres