Towards a unified theory of logic programming semantics: Level mapping characterizations of selector generated models

Currently, the variety of expressive extensions and different semantics created for logic programs with negation is diverse and heterogeneous, and there is a lack of comprehensive comparative studies which map out the multitude of perspectives in a uniform way. Most recently, however, new methodologies have been proposed which allow one to derive uniform characterizations of different declarative semantics for logic programs with negation. In this paper, we study the relationship between two of these approaches, namely the level mapping characterizations due to [Hitzler and Wendt 2005], and the selector generated models due to [Schwarz 2004]. We will show that the latter can be captured by means of the former, thereby supporting the claim that level mappings provide a very flexible framework which is applicable to very diversely defined semantics.Comment: 17 page

PROGRAMMING REACTIVE SYSTEMS IN TEMPORAL LOGIC

Information Systems Working Papers Serie

ON THE EXPRESSIVE POWER OF INFINITE TEMPORAL DATABASES

We discuss different techniques for representing infinite temporal data. There are two basic approaches: A procedural description, as used in production systems, and represented, in this paper, by a version of Datalog. The second approach is a more declarative method, using some form of temporal logic programming. We examine several versions of each approach, and compare their expressive power, i.e., what temporal data each formalism can capture.Information Systems Working Papers Serie

Combining Relational Algebra, SQL, Constraint Modelling, and Local Search

The goal of this paper is to provide a strong integration between constraint modelling and relational DBMSs. To this end we propose extensions of standard query languages such as relational algebra and SQL, by adding constraint modelling capabilities to them. In particular, we propose non-deterministic extensions of both languages, which are specially suited for combinatorial problems. Non-determinism is introduced by means of a guessing operator, which declares a set of relations to have an arbitrary extension. This new operator results in languages with higher expressive power, able to express all problems in the complexity class NP. Some syntactical restrictions which make data complexity polynomial are shown. The effectiveness of both extensions is demonstrated by means of several examples. The current implementation, written in Java using local search techniques, is described. To appear in Theory and Practice of Logic Programming (TPLP)Comment: 30 pages, 5 figure

VALIDATING REQUIREMENTS SPECIFICATIONS STATED IN KNOWLEDGE REPRESENTATION LANGUAGE TEMPLAR

Techniques for analysis and validation of software requirements specifications written in the knowledge representation language Templar are presented. Templar specifications are analyzed in terms of ambiguity, non-minimality, contradiction, incompleteness, and redundancy. Since Templar is a powerful knowledge representation language supporting a rich set of modeling primitives, it is difficult to reason directly on Templar specifications. To solve this problem, Templar specifications are mapped into equivalent temporal logic programs which are analyzed in terms the criteria listed above. However, it is hard to reason about Templar specifications because some of the criteria cannot be formally proven, and the verification of other criteria constitute undecidable or intractable problems. To overcome these difficulties, we consider a set of tractable conditions for each criteria, which serve as "alarms" for the user. If a condition is violated then it means that the specification either definitely has or potentially can have a problem. Furthermore, the user is notified about the source and the nature of the problem in certain cases.Information Systems Working Papers Serie

MODELING DYNAMICS OF DATABASES WITH RELATIONAL DISCRETE EVENT SYSTEMS AND MODELS

Behavior of relational databases is studied within the framework of Relational Discrete Event Systems (RDESes) and Models (RDEMs). Three behavior specification methods based on production systems, recurrence equations, and Petri nets are defined and their expressive powers are compared. Production system RDEM is extended to support non-determinism, and various deterministic and non-deterministic production system interpreters are introduced and formally compared in terms of their expressive power. It is shown that the parallel deterministic interpreter has more expressive power than other interpreters including an OPS5-like interpreter. Since it is also parallel, this makes the parallel deterministic interpreter a very attractive interpreter for production systems.Information Systems Working Papers Serie

Negation by default and unstratifiable logic programs

AbstractThe default approach to the theory of logic programs (and deductive databases) is based on the interpretation of negation by default rules. Default logic is a well-suited formalism to express the Closed World Assumption and to define the declarative semantics of stratifiable logic programs. The case of disjunctive consequences in rules is treated. General logic programs may not have a meaning with respect to default semantics. The contribution of the paper is to exhibit an interesting class of programs having a default semantics, called effectively stratifiable programs. This time, disjunctive consequences are not considered. Effective stratification is a weaker constraint than stratification, local stratification and weak stratification. Besides enlarging the class of stratifiable logic programs, the paper contributes to provide a constructive definition of well-founded models of logic programs. The class of effectively stratifiable logic programs matches the class of programs having a total well-founded model and in general, the default semantics extends the well-founded semantics