Extending Horn Clause Theories by Reflection Principles
نویسندگان
چکیده
In this paper, we introduce logical reeection as a principled way to empower the representation and reasoning capabilities of logic programming systems. In particular, reeection principles take the role of axiom schemata of a particular form that, once added to a given logic program (the basic theory, or the initial axioms), enlarge the set of consequences sanctioned by those initial axioms. The main advantage of this approach is that it is much easier to write a basic theory and then to augment it with condensed axiom schemata, than it is to write a corresponding large (or even innnite) set of axioms in the rst place. Moreover, the well-established semantic properties of Horn clauses, carry over to Horn clauses with reeection. In fact, the semantics of Reeective SLD Resolution and the semantics of the Reeective Least Herbrand Model are obtained by making slight variations to, respectively , the procedural and the declarative semantics classically deened for Horn clauses. We present a complete formalization of this concept of reeection, that should constitute a simple way of understanding re-ective programs; and a description of how reeection allows one to treat uniformly diierent application areas. To support this claim, the following three case studies will be discussed: metalevel reasoning; reasoning with multiple communicating theories (agents); and analogical reasoning. For each of these areas, the choice of a suitable reeection principle is shown, which tries to capture the speciicity of the problem domain.
منابع مشابه
Tree Automata with Equality Constraints Modulo Equational Theories
This paper presents new classes of tree automata combining automata with equality test and automata modulo equational theories. We believe that this class has a good potential for application in e.g. software verification. These tree automata are obtained by extending the standard Horn clause representations with equational conditions and rewrite systems. We show in particular that a generalize...
متن کاملF . Jacquemard , M . Rusinowitch and L . Vigneron Tree automata with equality constraints modulo equational theories Research Report LSV - 05 - 16 August 2005
This paper presents new classes of tree automata combining automata with equality test with automata modulo equational theories. These tree automata are obtained by extending their standard Horn clause representations with equational conditions and monadic rewrite systems. We show in particular that the general membership problem is decidable by proving that the saturation of tree automata pres...
متن کاملReflection in membership equational logic, many-sorted equational logic, Horn logic with equality, and rewriting logic
We show that the generalized variant of formal systems where the underlying equational specifications are membership equational theories, and where the rules are conditional and can have equations, memberships and rewrites in the conditions is reflective. We also show that membership equational logic, many-sorted equational logic, and Horn logic with equality are likewise reflective. These resu...
متن کاملInductive Learning from Good Examples
We study what kind of data may ease the computational complexity of learning of Horn clause theories (in Gold's paradigm) and Boolean functions (in PAC-learning paradigm). We give several deenitions of good data (basic and generative representative sets), and develop data-driven algorithms that learn faster from good examples, and degenerate to learn in the limit from the \worst" possible examp...
متن کاملA Tractable Class of Abduction Problems
literal: Let p be a proposition. Then p and -p are literals. clause: A clause is a disjunction of literals. Horn Clause: A Horn Clause is a clause in which there is at most one positive literal. definite clause: A definite clause is a Hom Clause in which there is exactly one positive literal. A definite clause such as can also be written as We call pi the head of the clause, and the conjunction...
متن کامل