Logic Programming with Default, Weak and Strict Negations

This paper treats logic programming with three kinds of negation: default, weak and strict negations. A 3-valued logic model theory is discussed for logic programs with three kinds of negation. The procedure is constructed for negations so that a soundness of the procedure is guaranteed in terms of 3-valued logic model theory.Comment: 14 pages, to appear in Theory and Practice of Logic Programming (TPLP

Normality Operators and Classical Collapse

In this paper, we extend the expressive power of the logics K3, LP and FDE with anormality operator, which is able to express whether a for-mula is assigned a classical truth value or not. We then establish classical recapture theorems for the resulting logics. Finally, we compare the approach via normality operator with the classical collapse approach devisedby Jc Beall

Transforming Normal Programs by Replacement

The replacement transformation operation, already defined in [28], is studied wrt normal programs. We give applicability conditions able to ensure the correctness of the operation wrt Fitting's and Kunen's semantics. We show how replacement can mimic other transformation operations such as thinning, fattening and folding, thus producing applicability conditions for them too. Furthermore we characterize a transformation sequence for which the preservation of Fitting's and Kunen's semantics is ensured

Transforming acyclic programs

An unfold/fold transformation system is a source-to-source rewriting methodology devised to improve the efficiency of a program. Any such transformation should preserve the main properties of the initial program: among them, termination. In the field of logic programming, the class of acyclic programs plays an important role in this respect, since it is closely related to the one of terminating programs. The two classes coincide when negation is not allowed in the bodies of the clauses. We prove that the Unfold/Fold transformation system defined by Tamaki and Sato preserves the acyclicity of the initial program. From this result, it follows that when the transformation is applied to an acyclic program, then the finite failure set for definite programs is preserved; in the case of normal programs, all major declarative and operational semantics are preserved as well. These results cannot be extended to the class of left-terminating programs without modifying the definition of the transformation

Nonmonotonic Trust Management for P2P Applications

Community decisions about access control in virtual communities are non-monotonic in nature. This means that they cannot be expressed in current, monotonic trust management languages such as the family of Role Based Trust Management languages (RT). To solve this problem we propose RT-, which adds a restricted form of negation to the standard RT language, thus admitting a controlled form of non-monotonicity. The semantics of RT- is discussed and presented in terms of the well-founded semantics for Logic Programs. Finally we discuss how chain discovery can be accomplished for RT-.Comment: This paper appears in the proceedings of the 1st International Workshop on Security and Trust Management (STM 2005). To appear in ENTC