Transitive Closure, Answer Sets and Predicate Completion

Transitive Closure, Answer Sets and Predicate Completion

Transitive Closure, Answer Sets and Predicate Completion

We prove that the usual logic programming definition of transitive closure is correct under the answer set semantics, and investigate under what conditions it is correct under the completion semantics. That definition is allowed here to be combined with an arbitrary set of rules that may contain negation as failure, not merely with a set of facts. This work is motivated by applications to answe...

Tight logic programs

This note is about the relationship between two theories of negation as failure—one based on program completion, the other based on stable models, or answer sets. François Fages showed that if a logic program satisfies a certain syntactic condition, which is now called “tightness,” then its stable models can be characterized as the models of its completion. We extend the definition of tightness...

A Logic and Decision Procedure for Predicate Abstraction of Heap-Manipulating Programs

An important and ubiquitous class of programs are heap-manipulating programs (HMP), which manipulate unbounded linked data structures by following pointers and updating links. Predicate abstraction has proved to be an invaluable technique in the field of software model checking; this technique relies on an efficient decision procedure for the underlying logic. The expression and proof of many i...

Properties of Binary Transitive Closure Logics over Trees

Binary transitive closure logic (FO∗ for short) is the extension of first-order predicate logic by a transitive closure operator of binary relations. Deterministic binary transitive closure logic (FOD∗) is the restriction of FO∗ to deterministic transitive closures. It is known that these logics are more powerful than FO on arbitrary structures and on finite ordered trees. It is also known that...