Jürgen Dix

Multi-Agent Programming

ion keeping the agent abstraction level e.g. no agents sharing and calling OO objects effective programming models for controllable and observable computational entities Modularity away from the monolithic and centralised view Orthogonality wrt agent models, architectures, platforms support for heterogeneous systems

A Classification Theory Of Semantics Of Normal Logic Programs: I. Strong Properties

Our aim in this article is to present a method for classifying and characterizing the various different semantics of logic programs with negation that have been considered in the last years. Instead of appealing to more or less questionable intuitions, we take a more structural view: our starting point is the observation that all semantics induce in a natural way non-monotonic entailment relations “ |˜ ”. The novel idea of our approach is to ask for the properties of these |˜ -relations and to use them for describing all possible semantics. The main properties discussed in this paper are adaptations of rules that play a fundamental role in general non-monotonic reasoning: Cumulativity and Rationality. They were introduced and investigated by Gabbay, Kraus, Lehmann, Magidor and Makinson. We show that the 3-valued version COMP 3 of Clarks completion, the stratified semantics M supp P as well as the well-founded semantics WFS and two extensions of it behave very regular: they are cumulative, rational and one of them is even supraclassical. While Pereiras recently proposed semantics O-SEM is not rational it is still cumulative. Cumulativity fails for the regular semantics REG-SEM of You/Yuan (recently shown to be equivalent to three other proposals). In a second article we will supplement these strong rules with a set of weak rules and consider the problem of uniquely describing a given semantics by its strong and weak properties together.

Characterizations of the disjunctive stable semantics by partial evaluation

There are three most prominent semantics defined for certain subclasses of disjunctive logic programs: GCWA (for positive programs), PERFECT (for stratified programs), and STABLE (defined for the whole class of all disjunctive programs). While there are various competitors based on 3-valued models, notably WFS and its disjunctive counterparts, there are no other semantics consisting of two-valued models. We argue that the reason for this is the Partial Evaluation property (also called Unfolding or Partial Deduction) well known from logic programming. In fact, we prove characterizations of these semantics and show that if a semantics SEM satisfies Partial Evaluation and Elimination of Tautologies, then (1) SEM is based on two-valued minimal models for positive programs, and (2) if SEM satisfies in addition Elimination of Contradictions, it is based on stable models. We also show that if we require Isomorphy and Relevance, then STABLE is completely determined on the class of all stratified disjunctive logic programs.

Characterizations of the Disjunctive Well-Founded Semantics: Confluent Calculi and Iterated GCWA

Recently Brass and Dix introduced the semantics D-WFS for general disjunctive logic programs. The interesting feature of this approach is that it is both semantically and proof-theoretically founded. Semantically, D-WFS is invariant under some natural declarative principles. Proof-theoretically, any program Φ is associated a normalform Φ, called the residual program, by a nontrivial bottom-up construction using least fixpoints of two monotonic operators.We show in this paper that the original calculus, consisting of some simple transformations, has a very strong and appealing property: it is confluent and terminating. This means that all the transformations can be applied in any order: whenever we arrive at an irreducible program (no more transformation is applicable), this program is already uniquely determined and coincides with the normalform res(Φ) Moreover, for fair sequences it is also strongly terminating: every fair sequence of transformations leads to normalform res(Φ). Another feature of our approach is that D-WFS can be read off from res(Φ) immediately in a very simple way. No proper subset of the calculus has these properties – only when we restrict to certain subclasses of programs.We also give an equivalent characterization of D-WFS in terms of iterated minimal model reasoning with respect to positive programs. This construction is a generalization of a description of the well-founded semantics: we introduce a very simple and neat construction of a sequence Di that eventually stops and represents the set of derivable disjunctions.Both characterizations open the way for efficient implementations. The first does so because the ordering of the transformations does not matter: we are free to choose always the “best” transformation, which maximally reduces the program. The second does so because special methods from circumscription, in particular a sophisticated minimal model reasoner for positive programs, might be useful.

Towards an environment interface standard for agent platforms

We introduce an interface for connecting agent platforms to environments. This interface provides generic functionality for executing actions and for perceiving changes in an agent’s environment. It also provides support for managing an environment, e.g., for starting, pausing and terminating it. Among the benefits of such an interface are (1) standard functionality is provided by the interface implementation itself, and (2) agent platforms that support the interface can connect to any environment that implements the interface. This significantly reduces effort required from agent and environment programmers as the environment code needed to implement the interface needs to be written only once. We propose that the interface presented may be used as a standard that enables agents to control entities in environments. Our starting point for designing such a generic interface is based on a careful study of the various interfaces used by different agent programming languages to connect agent programs to environments. We discuss several case studies that use our interface (an elevator simulator, the well-known agent contest, and an implementation of the interface to connect agents to bots in Unreal Tournament 2004).

Relating defeasible and normal logic programming through transformation properties

This paper relates the Defeasible Logic Programming (DeLP) framework and its semantics SEMDeLP to classical logic programming frameworks. In DeLP, we distinguish between two different sorts of rules: strict and defeasible rules. Negative literals (∼A) in these rules are considered to represent classical negation. In contrast to this, in normal logic programming (NLP), there is only one kind of rules, but the meaning of negative literals (not A) is different: they represent a kind of negation as failure, and thereby introduce defeasibility. Various semantics have been defined for NLP, notably the well-founded semantics (WFS) (van Gelder et al., Proceedings of the Seventh Symposium on Principles of Database Systems, 1988, pp. 221-230; J. ACM 38 (3) (1991) 620) and the stable semantics Stable (Gelfond and Lifschitz, Fifth Conference on Logic Programming, MIT Press, Cambridge, MA, 1988, pp. 1070-1080; Proceedings of the Seventh International Conference on Logical Programming, Jerusalem, MIT Press, Cambridge, MA, 1991, pp. 579-597).In this paper we consider the transformation properties for NLP introduced by Brass and Dix (J. Logic Programming 38(3) (1999) 167) and suitably adjusted for the DeLP framework. We show which transformation properties are satisfied, thereby identifying aspects in which NLP and DeLP differ. We contend that the transformation rules presented in this paper can help to gain a better understanding of the relationship of DeLP semantics with respect to more traditional logic programming approaches. As a byproduct, we obtain the result that DeLP is a proper extension of NLP.

A general Approach to Bottom-Up Computation of Disjunctive Semantics

Our goal is to derive bottom-up query-evaluation algorithms from abstract properties of the underlying negation semantics. In this paper, we demonstrate our approach for the disjunctive stable model semantics, but the ideas are applicable to many other semantics as well. Our framework also helps to understand and compare other proposed query evaluation algorithms. It is based on the notion of conditional facts, developed by Bry and Dung/Kanchansut. We start by computing a “residual program” and show that it is equivalent to the original program under very general conditions on the semantics (which are satisfied, e.g., by the well-founded, stable, stationary, and static semantics). Many queries can already be answered on the basis of the residual program. For the remaining literals, we propose to use an appropriate completion of the residual program, which syntactically characterizes the intended models. In the case of the stable model semantics, we utilize an interesting connection to Clarks completion.

A general theory of confluent rewriting systems for logic programming and its applications

Abstract Recently, Brass and Dix showed (J. Automat. Reason. 20(1) (1998) 143–165) that the well founded semantics WFS can be defined as a confluent calculus of transformation rules. This led not only to a simple extension to disjunctive programs (J. Logic Programming 38(3) (1999) 167–213), but also to a new computation of the well-founded semantics which is linear for a broad class of programs. We take this approach as a starting point and generalize it considerably by developing a general theory of Confluent LP-systems CS . Such a system CS is a rewriting system on the set of all logic programs over a fixed signature L and it induces in a natural way a canonical semantics. Moreover, we show four important applications of this theory: (1) most of the well-known semantics are induced by confluent LP-systems, (2) there are many more transformation rules that lead to confluent LP-systems, (3) semantics induced by such systems can be used to model aggregation, (4) the new systems can be used to construct interesting counterexamples to some conjectures about the space of well-behaved semantics.

Partial Evaluation and Relevance for Approximations of Stable Semantics

There is no doubt that STABLE and WFS are among the dominant semantics for logic programs. While WFS has many nice structural properties, it is very weak. STABLE allows to derive more atoms, but may become inconsistent and it is not relevant, i.e. the truth value of an atom does not only depend on the call-graph below it. In this paper we consider the problem of defining approximations of STABLE that are both relevant and satisfy a general partial deduction property.

Model Checking Logics of Strategic Ability: Complexity*

This chapter is about model checking and its complexity in some of the main temporal and strategic logics, e.g. LTL, CTL, and ATL. We discuss several variants of ATL (perfect vs. imperfect recall, perfect vs. imperfect information) as well as two different measures for model checking with concurrent game structures (explicit vs. implicit representation of transitions). Finally, we summarize some results about higher order representations of the underlying models.