Designing Dependencies

Given a binary recursively enumerable relation R, one or more logic programs over a language L can be constructed and interconnected to produce a dependency relation D on selected predicates within the Herbrand base BL of L isomorphic to R. D can be, optionally, a positive, negative or mixed dependency relation. The construction is applied to representing any effective game of the type introduced by Gurevich and Harrington, which they used to prove Rabin\u27s decision method for S2S, as the dependency relation of a logic program. We allow games over an infinite alphabet of possible moves. We use this representation to reveal a common underlying reason, having to do with the shape of a program\u27s dependency relation, for the complexity of several logic program properties

The Complexity of Local Stratification

The class of locally stratified logic programs is shown to be Π11-complete by the construction of a reducibility of the class of infinitely branching nondeterministic finite register machines.nondeterministic finite register machines

Strong Completeness Results for Paraconsistent Logic Programming

In [6], we introduced a means of allowing logic programs to contain negations in both the head and the body of a clause. Such programs were called generally Horn programs (GHPs, for short). The model-theoretic semantics of GHPs were defined in terms of four-valued Belnap lattices [5]. For a class of programs called well-behaved programs, an SLD-resolution like proof procedure was introduced. This procedure was proven (under certain restrictions) to be sound (for existential queries) and complete (for ground queries). In this paper, we remove the restriction that programs be well-behaved and extend our soundness and completeness results to apply to arbitrary existential queries and to arbitrary GHPs. This is the strongest possible completeness result for GHPs. The results reported here apply to the design of very large knowledge bases and in processing queries to knowledge bases that possibly contain erroneous information

Arithmetic Classification of Perfect Models of Stratified Programs (Addendum)

RECURSION-FREE PROGRAMS The following section completes the analysis of arithmetic complexity of perfect models and has been inadvertently omitted in the previous version of the paper. We say that a general program P is recursion-free if in its dependency graph Dp there is no cycle. Clearly recursion-free programs form a subclass of stratified programs. Recursion-free programs form a very simple generalization of the class of hierarchical programs introduced in [C78]. Hierarchical programs satisfy an additional condition on variable occurrences in clauses that prevents floundering, i.e. a forced selection of a non-ground negative literal in an SLDNF- derivation. In this section we study the complexity of perfect models of recursion-free programs

A Logic Grammar Foundation for Document Representation and Document Layout

We present a powerful grammar-based paradigm for electronic document markup: coordinated definite clause translation grammars. This markup is of a declarative character, being, in effect, a collection of constraints on the logical and physical structure of documents. To the best of our knowledge, coordinated grammars and their parsers can accommodate all of the descriptive and layout processing functionality enjoyed by extant electronic markup languages. We describe an operational prototype that demonstrates the feasibility of a syntax-directed basis for formalizing and realizing document layout

A Logic Programming Elucidation of ODA - Document Descriptions and Processes

We are pursuing a programme of research in document representation. The principal aim of this research is to develop a document description language that has a precise formal semantics, that is fully expressive of the constructs typical of traditional (procedural) document description languages, that is constraint-based, and that cleanly separates specifications of form and content. The research is currently in the first of three envisioned three phases. In the first phase we are formalising the Office Document Architecture (ODA) by faithfully translating ODA document descriptions into logic programmes. The transition utilizes highly restricted forms of Prolog programmes.1 In the second phase we will explore various enhancements of ODA\u27s expressive power that are immediately apparent upon freeing the translation from having to adhere to the initial restrictive conventions. Finally, we will explore and articulate a constraint logic programming language having “built-in constructs for expressing both primitive and composite document description concepts. In the present essay we sketch our translation (into a DCG framework) of ODA document descriptions and (layout) processes. As it turns out the resulting translation is closely related to so called functional attribute grammars [4]. Indeed, we hope eventually to exploit that relationship to enable efficient interpretation of the resulting translation. For now, however, we hope to convince our readers that (definite clause) grammars are a natural and powerful generalisation of the ODA framework, and that the ODA layout process can be specified entirely by declarative means by appealing to properties of the grammars in question

Simulations Between Programs as Cellular Automata

We present cellular automata on appropriate digraphs and show that any covered normal logic program is a cellular automaton. Seeing programs as cellular automata shifts attention from classes of Herbrand models to orbits of Herbrand interpretations. Orbits capture both the declarative, model-theoretic meaning of programs as well as their inferential behavior. Logically and intentionally different programs can produce orbits that simulate each other. Simple examples of such behavior are compellingly exhibited with space-time diagrams of the programs as cellular automata. Construing a program as a cellular automaton leads to a general method for simulating any covered program with a Horn clause program