Horn Clause Logic Programming Research Articles

Proceedings of the First Workshop on Coalgebra, Horn Clause Logic Programming and Types

Proceedings of the First Workshop on Coalgebra, Horn Clause Logic Programming and Types

Proceedings of the First Workshop on Coalgebra, Horn Clause Logic Programming and Types

Proceedings of the First Workshop on Coalgebra, Horn Clause Logic Programming and Types

Proceedings of the First Workshop on Coalgebra, Horn Clause Logic Programming and Types

Proceedings of the First Workshop on Coalgebra, Horn Clause Logic Programming and Types

Proceedings of the First Workshop on Coalgebra, Horn Clause Logic Programming and Types

Proceedings of the First Workshop on Coalgebra, Horn Clause Logic Programming and Types

Proceedings of the First Workshop on Coalgebra, Horn Clause Logic Programming and Types

Proceedings of the First Workshop on Coalgebra, Horn Clause Logic Programming and Types

On the algebraic structure of declarative programming languages

We develop an algebraic framework, Logic Programming Doctrines, for the syntax, proof theory, operational semantics and model theory of Horn Clause logic programming based on indexed premonoidal categories. Our aim is to provide a uniform framework for logic programming and its extensions capable of incorporating constraints, abstract data types, features imported from other programming language paradigms and a mathematical description of the state space in a declarative manner. We define a new way to embed information about data into logic programming derivations by building a sketch-like description of data structures directly into an indexed category of proofs. We give an algebraic axiomatization of bottom-up semantics in this general setting, describing categorical models as fixed points of a continuous operator.

Non-Horn clause logic programming

There has been active work to extend the Prolog style Horn clause logic programming to non-Horn clauses. In this paper, we analyze and compare several such extensions using an analytical approach. All the extensions discussed behave exactly like Prolog when only Horn clauses are involved. The purpose is to understand the computational complexity of these inference systems when non-Horn clauses are present. The analyses do not necessarily prove that any one system is better than the others all the time. But they do suggest when one system may be better than the others for some particular kind of problems. They also help to discover some interesting properties of some extensions and suggest a possible syntactic transformation on problems to improve the performance of some extensions.

A high-level Petri net for goal-directed semantics of Horn clause logic

A new high level Petri net (HLPN) model is introduced as a graphical syntax for Horn clause logic (HCL) programs. We call these nets: Horn clause logic goal directed nets (HCLGNs). It is shown that there is a bijection between the queried definite programs and the class of HCLGNs. In addition, a visualization of SLD resolution is realized through the enabling and firing rules and net markings. The correctness of these rules with respect to SLD resolution is also proven. We model SLD refutations and failing computations. It is shown how HCLGNs can be used to model built in atoms and provide a new AND/OR parallel execution model. Recently, several software packages (graphical editors) have become available for editing and executing HLPNs. The simulation capabilities of the HLPN software offer opportunities to perform automated, interactive code walk throughs and also have potential for providing a framework for visual debugging environments. However, HCLGNs differ from the major classes of HLPNs for which software tools have been developed in primarily two ways: the tokens in the markings can have variables; and the firing of a transition may not only update the marking of the adjacent places, but may instantiate variables in tokens in the markings of places that are non adjacent to the fired transition. Thus, the existing packages can only provide graphical syntax editing and are not appropriate for graphical simulation of HCLGNs. We provide an algebraic characterization of HCLGNs that can serve as a design guideline for implementing HCLGNs.

On computability by logic programs

The problem of computational completeness of Horn clause logic programs is revisited. The standard results on representability of all computable predicates by Horn clause logic programs are not related to the real universe on which logic programs operate. SLD-resolution, which is the main mechanism to execute logic programs, may give answer substitutions with variables. As the main result we prove that computability by Horn clause logic programs is equivalent to standard computability over the Herbrand universe with variables. The semantics we use isS-semantics introduced by Falaschi et al. [3]. As an application of the main result we prove the existence of a metainterpreter for a sublanguage of real Prolog, written in the language of Horn clauses with the S-semantics. We also show that the traditional semantics of Prolog do not reflect its computational behavior from the viewpoint of recursion theory.

Suprema of Open and Closed Formulas and Their Application to Resolution

We discuss an algebra of open formulas, SOAF. The algebra is equipped with the operator mgi-o , which computes suprema of sets of open formulas, ordered according to a weak form of instance ordering. Rules to compute such points are provided. These rules supply a computation procedure to unify open formulas. Next, we consider an algebra of closed formulas, SCAF. It has an operator mgi-c , which computes suprema of set of formulas ordered according to the instance preordering. We give rules to compute such points. These rules supply a computation procedure to unify closed formulas. Relations between these operators and unification in open and closed formulas, and weak unification in closed formulas, are addressed. Also, we consider clausal formulas and apply these considerations to the resolution process. This provides a rule alternative to resolution and shows that resolvents can be expressed and effectively obtained as suprema of closed formulas. The new rule need not resort to renaming, unification. and instantiation as first class operations. Finally, applications to resolution in Horn clause logic and logic programming are discussed. This leads to a more compact theory of logic programming, in which, for instance, the domain of substitutions is eliminated.

Preference logics: Towards a unified approach to nonmonotonicity in deductive reasoning

The notion ofpreference is central to most forms of nonmonotonic reasoning. Shoham, in his dissertation, used this notion to give a single semantical point of view from which most nonmonotonic reasoning systems could be studied. In this paper, we study the notion of preference closely and devise a class of logics of preference that extract the logicalcore of the notion of preference. Earlier attempts have been largely unsuccessful, because of adoption as matters of logic of certain theory-specific preference principles such asasymmetry andtransitivity. Soundness, completeness and decidability proofs for the logics are given. We define the notion of a preferential theory and reframe nonmonotonicity as a symbolic optimization problem where defaults are coded aspreference criteria which place preference orders on the models of a first-order theory. We study the relationship between normal default theories and show the correspondence between models of extensions and optimal worlds. We give a preferential account of some forms of circumscription. Thelocal nature of preference logic is contrasted with the global notion of normality and preference that is used by conditional logics of normality and cumulative inference operations. In related papers, we give a completely declarative semantics for the stable models of normal logic programs, a deontic logic based on preferences that is free of the anomalies of standard deontic logic, and extend Horn clause logic programming to impose partial orders on the bodies of clauses as declarative specification of the relaxation criteria for the truth-hood of the heads.

High-level Petri net model of logic program with negation

The formalism of nonmonotonic reasoning has been integrated into logic programming to define semantics for logic program with negation. Because a Petri net provides a uniform model for both the logic of knowledge and the control of inference, the class of high-level Petri nets called predicate/transition nets (PrT-nets) has been employed to study production rule based expert systems and Horn clause logic programs. We show that a PrT-net can implement the nonmonotonicity associated with a logic program with negation as well as the monotonicity of Horn clause logic program. In particular, we define a semantics for a normal logic program and implement it with PrT-net. We demonstrate that in the presence of inconsistency in a normal logic program, the semantics still works well by deducing meaningful answers. The variations and potential applications of the PrT-net are also addressed. >

Circumscribing embedded implications (without stratifications)

This paper is a study of circumscription, not in classical logic, as usual, but in intuitionistic logic. We first review the intuitionistic circumscription of Horn clause logic programs, which was discussed in previous work, and we then consider the larger class of embedded implications. The ordinary circumscription axiom turns out to be inappropriate for this class of rules, and we analyze two alternatives: (1) prioritized circumscription, which works for stratified embedded implications; (2) partial circumscription, which is independent of the stratification. We then show that these two approaches coincide by identifying a single structure that serves as the final Kripke model for both circumscription axioms. This means that prioritized circumscription and partial circumscription entail exactly the same set of implicational queries. Several applications of these ideas are described, including (1) an interpretation of negation-as-failure, (2) a formalization of indefinite reasoning with definite rules, and (3) a methodology for analyzing inductive properties of PROLOG programs.

An implementation of pure Horn clause logic programming in a reduction system

Many reduction systems have been presented for implementing functional programming languages. We propose here an extension of a reduction architecture to realize a kind of logic programming — pure Horn clause logic programming. This is an attempt to approach amalgamation of the two important programming paradigms.

A bottom-up polymorphic type inference in logic programming

We present a type inference system for Horn clause logic programs, based on a bottom-up abstract interpretation technique. Through the definition of suitable abstract operators, we obtain an abstract immediate consequence operator map associated with the program to analyze. The least fixpoint of such an operator gives an approximated description, by means of types, of the success set of the program. By changing the abstract domain of types, we easily obtain different type inference systems. This is useful to make the inference appropriate for different purposes. Due to the semantic basis, the system declaratively handles type union and parametric polymorphism.

On the complexities of non-Horn Clause logic programming

There have been active work to extend the Prolog style Horn Clause logic programming to non-Horn clauses. In this paper, we will analyze the complexities of several such extensions. The purpose is to understand the computational complexity of these inference systems. The analyses do not prove that any one system is better than the others all the time. But they do suggest that one system may be better than the others for some particular problems. We also discuss the effect of caching.

Magic templates: a spellbinding approach to logic programs

We consider a bottom-up query-evaluation scheme in which facts of relations are allowed to have nonground terms. The magic-sets query- rewriting technique is generalized to allow arguments of predicates to be treated as bound even though the rules do not provide ground bindings for those arguments. In particular, we regard as “bound” any argument containing a function symbol or a variable that appears more than once in the argument list. Generalized “magic” predicates are thus defined to compute the set of all goals reached in a top-down exploration of the rules, starting from a given query goal; these goals are not facts of constants as in previous versions of the magic-sets algorithm. The magic predicates are then used to restrict a bottom-up evaluation of the rules so that there are no redundant actions; that is, every step of the bottom-up computation must be performed by any algorithm that uses the same sideways information-passing strategy (sips). The price paid, compared to previous versions of Magic Sets, is that we must store relations with nonground facts, and we must perform unifications, rather than equijoins, when evaluating the rules bottom-up. The method is applicable to general Horn-clause logic programs.

Non-Horn clause logic programming without contrapositives

We present an extension of Prolog-style Horn clause logic programming to full first order logic. This extension has some advantages over other such extensions that have been proposed. We compare this method with the model elimination strategy which Stickel has recently implemented very efficiently, and with Loveland's extension of Prolog to near-Horn clauses. This new method is based on the author's “simplified problem reduction format” but permits a better control of the splitting rule than does the simplified problem reduction format. In contrast to model elimination, this new method does not require the use of contrapositives of clauses, permitting a better control of the search. This method has been implemented in C Prolog and has turned out to be a respectable and surprisingly compact first-order theorem prover. This implementation uses depth-first iterative deepening and caching of answers to avoid repeated solution of the same subgoal. We show that the time and space used by this method are polynomial functions of certain natural parameters of the search space, unlike other known methods. We discuss the relation of these upper bounds to Savitch's theorem relating nondeterministic time to deterministic space.

Pseudo-Boolean valued prolog

A generalization of conventional Horn clause logic programming is proposed in which the space of truth values is a pseudo-Boolean or Heyting algebra, whose members may be thought of as evidences for propositions. A minimal model and an operational semantics is presented, and their equivalence is proved, thus generalizing the classic work of Van Emden and Kowalski.

A predicate-transition net model for parallel interpretation of logic programs

A predicate/transition net model for a subset of Horn clause logic programs is presented. The syntax, transformation procedure, semantics, and deduction process for the net model are discussed. A possible parallel implementation for the net model is described, which is based on the concepts of communicating processes and relations. The proposed net model offers a syntactical variant of Horn clause logic and has two distinctions from other existing schemes for the logic programs: representation formalism and the deduction method. The net model provides an approach towards the solutions of the separation of logic from control and the improvement of the execution efficiency through parallel processing for the logic programs. The abstract nature of the net model also lends itself to different implementation strategies.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>