35 research outputs found
The Limits of Horn Logic Programs
Given a sequence of Horn logic programs, the limit of
is the set of the clauses such that every clause in belongs
to almost every and every clause in infinitely many 's belongs
to also. The limit program is still Horn but may be infinite. In
this paper, we consider if the least Herbrand model of the limit of a given
Horn logic program sequence equals the limit of the least Herbrand
models of each logic program . It is proved that this property is not
true in general but holds if Horn logic programs satisfy an assumption which
can be syntactically checked and be satisfied by a class of Horn logic
programs. Thus, under this assumption we can approach the least Herbrand model
of the limit by the sequence of the least Herbrand models of each finite
program . We also prove that if a finite Horn logic program satisfies
this assumption, then the least Herbrand model of this program is recursive.
Finally, by use of the concept of stability from dynamical systems, we prove
that this assumption is exactly a sufficient condition to guarantee the
stability of fixed points for Horn logic programs.Comment: 11 pages, added new results. Welcome any comments to
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Description of Fuzzy First-Order Modal Logic Based on Constant Domain Semantics
Abstract. As an extension of the traditional modal logic, the fuzzy first-order modal logic is discussed in this paper. A description of fuzzy first-order modal logic based on constant domain semantics is given, and a formal system of fuzzy reasoning based on the semantic information of models of first-order modal logic is established. It is also introduced in this paper the notion of the satisfiability of the reasoning system and some properties associated with the satisfiability are proved
The Correspondence between Propositional Modal Logic with Axiom and the Propositional Logic
Part 5: Automatic ReasoningInternational audienceThe propositional modal logic is obtained by adding the necessity operator β‘ to the propositional logic. Each formula in the propositional logic is equivalent to a formula in the disjunctive normal form. In order to obtain the correspondence between the propositional modal logic and the propositional logic, we add the axiom to K and get a new system Kβ+β. Each formula in such a logic is equivalent to a formula in the disjunctive normal form, where β‘k(kββ₯β0) only occurs before an atomic formula p, and only occurs before a pseudo-atomic formula of form β‘k p. Maximally consistent sets of Kβ+β have a property holding in the propositional logic: a set of pseudo-atom-complete formulas uniquely determines a maximally consistent set. When a pseudo-atomic formula β‘k pi (k,iββ₯β0) is corresponding to a propositional variable qki, each formula in Kβ+β then can be corresponding to a formula in the propositional logic Pβ+β. We can also get the correspondence of models between Kβ+β and Pβ+β. Then we get correspondences of theorems and valid formulas between them. So, the soundness theorem and the completeness theorem of Kβ+β follow directly from those of Pβ+β