Towards resource handling in logic programming: The PPL framework and its semantics

Most of the theoretical work on the semantics of logic programs assumes an interpreter that provides a complete resolution procedure. In contrast, for reasons of efficiency, most logic programming languages are built around incomplete procedures. This difference is rooted in Prolog, which evaluates resolvent trees in a depth-first rather than a breadth-first order. The gap is widened by some equational logic languages, which combine the incompleteness of depth-first evaluation with incomplete approximations to equational unification. Because of this gap, it is unsound to reason about logic programs using their declarative semantics. This in turn makes it difficult to develop abstraction mechanisms that can be used to partition a logic program into independently specifiable modules.

We present a probabilistic logic programming framework that allows the representation of conditional probabilities. While conditional probabilities are the most commonly used method for representing uncertainty in probabilistic expert systems, they have been largely neglected by work in quantitative logic programming. We define a fixpoint theory, declarative semantics, and proof procedure for the new class of probabilistic logic programs. Compared to other approaches to quantitative logic programming, we provide a true probabilistic framework with potential applications in probabilistic expert systems and decision support systems. We also discuss the relationship between such programs and Bayesian networks, thus moving toward a unification of two major approaches to automated reasoning.

On the semantics of μ Log

A formal model of analogy is introduced in the logic programming setting, and an analogical reasoning program (called DIANA, i.e. Declarative Inference by ANAlogy) is developed in accordance with precise procedural and declarative semantics. Given the source and target domains of analogy as two logic programsPs andPt, together with a specificationS of the analogical correspondence between predicate symbols, atoms involving these symbols are analogically derived fromP=Ps ∪Pt givenS, which are not derivable fromPs orPt orPs ∪Pt alone. In this paper, the requirements of the analogical process are first stated. The declarative semantics of analogy is then given, by defining the least analogical model ofP as an extension of the classical semantics of Horn clauses. A procedural semantics is also described, in terms of an extension of SLD resolution. Both semantics rely on implicit analogical axioms defining the kind of analogical reasoning envisaged. The implementation of DIANA has been done in Reflective Prolog, a metalogic programming language previously developed by the first two authors. It is shown that analogical axioms can be viewed as an instance of reflection axioms used in Reflective Prolog. By exploiting this feature, the implementation of DIANA is argued to be sound w.r.t. the defined semantics. Examples of analogical reasoning in DIANA are also described. By comparison with the AI literature on analogy, it is claimed that this is the first approach which gives a declarative semantics to analogical reasoning, thanks to the possibility of carrying over in this field the basic logic programming concepts.

We introduce a generalized logic programming paradigm where programs,\nconsisting of facts and rules with the usual syntax, can be enriched by\nco-facts, which syntactically resemble facts but have a special meaning. As in\ncoinductive logic programming, interpretations are subsets of the complete\nHerbrand basis, including infinite terms. However, the intended meaning\n(declarative semantics) of a program is a fixed point which is not necessarily\nthe least, nor the greatest one, but is determined by co-facts. In this way, it\nis possible to express predicates on non well-founded structures, such as\ninfinite lists and graphs, for which the coinductive interpretation would be\nnot precise enough. Moreover, this paradigm nicely subsumes standard\n(inductive) and coinductive logic programming, since both can be expressed by a\nparticular choice of co-facts, hence inductive and coinductive predicates can\ncoexist in the same program. We illustrate the paradigm by examples, and\nprovide declarative and operational semantics, proving the correctness of the\nlatter. Finally, we describe a prototype meta-interpreter.\n

Institutions for logic programming

The problem of determining the correct declarative semantics for generalized logic programs is still open. In generalized logic programs the body of a rule may contain negated goals. Using a logical equivalence these programs may be viewed as disjunctive logic programs where the head of a rule may contain a disjunction of goals. We hope that a careful study of the declarative semantics of disjunctive logic programs will produce criteria for evaluating the different candidates for the semantics of generalized logic programs.A conceptual analysis leads to a semantical definition of the notion of a disjunctive deductive database as a generalization of the notion of a deductive database. It will be shown that the notion of a disjunctive deductive database is equivalent to the syntactical definition of a disjunctive logic program. We have characterized disjunctive deductive databases, i. e. theories which admit in each irreducible component a minimal Herbrand model and for which this property is preserved under the addition of new facts, as disjunctive logic programs. As a special case the result yields the known characterization of deductive databases, i. e. theories which admit a minimal Herbrand model and for which this property is preserved under the addition of new facts, as logic programs. In the presence of equations term structures i. e. extended Herbrand structures replace the Herbrand structures and h-core models replace the minimal models. Actually, the results could be proved in a more general context where pseudo term structures replace the term structures. In addition, there is an intermediate case where the irreducible components coincide with the connected components. Moreover, there are characterization results for the cases where the uniformity condition is not present.KeywordsLogic ProgramIrreducible ComponentTerm StructureCanonical ModelDeductive DatabaseThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Active Logic is a conceptual system, the principles of which are satisfied with formalisms of reasoning, which allow correlating the results of reasoning with moments in time and ensuring tolerance to contradictions. At present, tolerance to contradictions (paraconsistency) as applied to Active Logic systems has received theoretical justification in the works of the authors of this report and refers to the so-called formalisms of step theories, combining the principles of Active Logic and logical programming. In particular, it was proved that the argumentative semantics of the formalism of extended step theories, which have two types of negation and have more developed expressive capabilities, are paranormal. The formalism introduced in this paper has even greater expressive capabilities. Keeping all the controls for the process of reasoning in time, this formalism allows one to more adequately represent facts about the subject area by using the language of first-order logic instead of the language of propositional logic. For the formalism of extended step theories of the first order, a declarative semantics is proposed, its paraneosistance is shown, and the expressive possibilities of this formalism in relation to the tasks of action planning are demonstrated using the example of the monkey and the banana.KeywordsActive logicTime reasoningExtended first-order step theoriesDeclarative semanticsParaconsistencyArgumentative semantics

In previous work, we proposed a logic-based framework in which computation is the execution of actions in an attempt to make reactive rules of the formif antecedent then consequenttrue in a canonical model of a logic program determined by an initial state, sequence of events, and the resulting sequence of subsequent states. In this model-theoretic semantics, reactive rules are the driving force, and logic programs play only a supporting role. In the canonical model, states, actions, and other events are represented with timestamps. But in the operational semantics (OS), for the sake of efficiency, timestamps are omitted and only the current state is maintained. State transitions are performed reactively by executing actions to make theconsequentsof rules true whenever theantecedentsbecome true. This OS is sound, but incomplete. It cannot make reactive rules true by preventing theirantecedentsfrom becoming true, or by proactively making theirconsequentstrue before theirantecedentsbecome true. In this paper, we characterize the notion of reactive model, and prove that the OS can generate all and only such models. In order to focus on the main issues, we omit the logic programming component of the framework.

This paper extends fuzzy logic programs [12, 24] to allow the explicit representation of classical negation as well as non-monotonic negation, by introducing the notion of extended fuzzy logic programs. We present the fuzzy answer set semantics for the extended fuzzy logic programs, which is based on the classical answer set semantics of classical extended logic programs [7]. We show that the proposed semantics is a natural extension to the classical answer set semantics of classical extended logic programs [7]. Furthermore, we define fixpoint semantics for extended fuzzy logic programs with and without non-monotonic negation, and study their relationship to the fuzzy answer set semantics. In addition, we show that the fuzzy answer set semantics is reduced to the stable fuzzy model semantics for normal fuzzy logic programs introduced in [42]. The importance of that is computational methods developed for normal fuzzy logic programs can be applied to the extended fuzzy logic programs. Moreover, we show that extended fuzzy logic programs can be intuitively used for representing and reasoning about actions in fuzzy environment.

We introduce a new approach to probabilistic logic programming in which probabilities are defined over a set of possible worlds. More precisely, classical program clauses are extended by a subinterval of [0,1] that describes a range for the conditional probability of the head of a clause given its body. We then analyze the complexity of selected probabilistic logic programming tasks. It turns out that probabilistic logic programming is computationally more complex than classical logic programming, More precisely, the tractability of special cases of classical logic programming generally does not carry over to the corresponding special cases of probabilistic logic programming. Moreover, we also draw a precise picture of the complexity of deciding and computing tight logical consequences in probabilistic reasoning with conditional constraints in general. We then present linear optimization techniques for deciding satisfiability and computing tight logical consequencesof probabilistic logic programs. These techniques are efficient in the special case in which we have little relevant purely probabilistic knowledge. We finally show that probabilistic logic programming under certain syntactic and semantic restrictions is closely related to van Emden's quantitative deduction, and thus has computational properties similar to calssical logic programming. Based on this result, we present an efficient approximation technique for probabilistic logic programming.

Lawry's label semantics for modeling and computing with linguistic information in natural language provides a clear interpretation of linguistic expressions and thus a transparent model for real-world applications. Meanwhile, annotated logic programs (ALPs) and its fuzzy extension AFLPs have been developed as an extension of classical logic programs offering a powerful computational framework for handling uncertain and imprecise data within logic programs. This paper proposes annotated linguistic logic programs (ALLPs) that embed Lawry's label semantics into the ALP/AFLP syntax, providing a linguistic logic programming formalism for development of automated reasoning systems involving soft data as vague and imprecise concepts occurring frequently in natural language. The syntax of ALLPs is introduced, and their declarative semantics is studied. The ALLP SLD-style proof procedure is then defined and proved to be sound and complete with respect to the declarative semantics of ALLPs. © 2010 Wiley Periodicals, Inc.

Semantics of infinite tree logic programming

Lazy narrowing with simplification

Three-valued completion for abductive logic programs