This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.

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Practically all programming languages used in software engineering allow to split a program into several modules. For fully declarative and nonmonotonic logic programming languages, however, the modular structure of programs is hard to realise, since the output of an entire program cannot in general be composed from the output of its component programs in a direct manner. In this paper, we consider these aspects for the stable-model semantics of disjunctive logic programs (DLPs). We define the notion of a DLP-function, where a welldefined input/output interface is provided, and establish a novel module theorem enabling a suitable compositional semantics for modules. The module theorem extends the well-known splitting-set theorem and allows also a generalisation of a shifting technique for splitting shared disjunctive rules among components.

The stable model semantics of disjunctive logic programs is based on classical models which are minimal with respect to subset inclusion. As a consequence, every atom appearing in a disjunctive program is false by default. This is sometimes undesirable from the knowledge representation point of view and a more refined control of minimization is called for. Such features are already present in Lifschitz's parallel circumscription where certain atoms are allowed to vary or to have fixed values while all other atoms are minimized. In this paper, it is formally shown that the expressive power of minimal models is properly increased in the presence of varying atoms. In spite of this, we show how parallel circumscription can be embedded into disjunctive logic programming in a relatively systematic fashion using a linear and faithful, but non-modular translation. This enables the conscious use of varying atoms in disjunctive logic programs — leading to more elegant and concise problem representations in various domains.

In this paper we show that Datalog is well-suited as a temporal verification language. Datalog is a well-known database query language relying on the logic programming paradigm. We introduce Datalog LITE, a fragment of Datalog with negation, and present a linear time model checking algorithm for Datalog LITE. We show that Datalog LITE subsumes temporal languages such as CTL and the alternation-free -calculus, and in fact give easy syntactic characterizations of these temporal languages. We prove that Datalog LITE has the same expressive power as the alternation-free portion of guarded fixed point logic.

We survey recent results about the relation between Datalog and temporal verification logics. Datalog is a well-known database query language relying on the logic programming paradigm. We introduce Datalog LITE, a fragment of Datalog with well-founded negation, which has an easy stratified semantics and a linear time model checking algorithm. Datalog LITE subsumes temporal languages such as CTL and the alternation-free -calculus. We give easy syntactic characterizations of these temporal languages by fragments of Datalog LITE, and show that Datalog LITE has the same expressive power as the alternation-free portion of guarded fixed point logic.

Generalized quantifiers are an important concept in modeltheoretic logic which has applications in different fields such as linguistics, philosophical logic and computer science. In this paper, we consider a novel application in the field of logic programming, which has been presented recently. The enhancement of logic programs by generalized quantifiers is a convenient tool for interfacing extra-logical functions and provides a natural framework for the definition of modular logic programs.

Abstract. Recently, enabling modularity aspects in Answer Set Programming (ASP) has gained increasing interest to ease the composition of program parts to an overall program. In this paper, we focus on modular nonmonotonic logic programs (MLP) under the answer set semantics, whose modules may have contextually dependent input provided by other modules. Moreover, (mutually) recursive module calls are allowed. We define a model-theoretic semantics for this extended setting, show that many desired properties of ordinary logic programming generalize to our modular ASP, and determine the computational complexity of the new formalism. We investigate the relationship of modular programs to disjunctive logic programs with well-defined input/output interface (DLP-functions) and show that they can be embedded into MLPs.

Abstract. We present a principled framework for modular web rule bases, called MWeb. According to this framework, each predicate defined in a rule base is characterized by its defining reasoning mode, scope, and exporting rule base list. Each predicate used in a rule base is characterized by its requesting reasoning mode and importing rule base list. For legal MWeb modular rule bases S, the MWebAS and MWebWFS semantics of each rule base s ∈ S w.r.t. S are defined model-theoretically. These semantics extend the answer set semantics (AS) and the well-founded semantics with explicit negation (WFSX) on ELPs, respectively, keeping all of their semantical and computational characteristics. Our framework supports: (i) local semantics and different points of view, (ii) local closed-world and open-world assumptions, (iii) scoped negation-as-failure, (iv) restricted propagation of local inconsistencies, and (v) monotonicity of reasoning, for “fully shared ” predicates.

Abstract. We develop a module-based framework for constraint modeling where it is possible to combine different constraint modeling languages and exploit their strengths in a flexible way. In the framework a constraint model consists of modules with clear input/output interfaces. When combining modules, apart from the interface, a module is a black box whose internals are invisible to the outside world. Inside a module a chosen constraint language (approaches such as CP, ASP, SAT, and MIP) can be used. This leads to a clear modular semantics where the overall semantics of the whole constraint model is obtained from the semantics of individual modules. The framework supports multi-language modeling without the need to develop a complicated joint semantics and enables the use of alternative semantical underpinnings such as default negation and classical negation in the same model. Furthermore, computational aspects of the framework are considered and, in particular, possibilities of benefiting from the known module structure in solving constraint models are studied. 1