Multi-Valued Symbolic Model-Checking: Fairness, Counter-Examples, Running Time Arie Gurfinkel Master of Science Graduate Department of Computer Science University of Toronto 2003 Multi-valued model-checking is an effective technique for reasoning about systems with incomplete or inconsistent information. In particular, it is well suited for reasoning about abstract, partial, and feature-based s...

Kleene’s strong three-valued logic extends naturally to a four-valued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it four-valued analogs of Kleene’s weak three-valued logic, and the asymmetric logic of Lisp are also available. We propose an extension of these ideas to the family of distributive bi...

We generalize the construction of lattice-valued models of set theory due to Takeuti, Titani, Kozawa and Ozawa to a wider class of algebras and show that this yields a model of a paraconsistent logic that validates all axioms of the negation-free fragment of Zermelo-Fraenkel set theory. §

We introduce an abstract algebraic structure — a lattice defined on a generalized truth value space of constructive logic. For background one can refer to the idea of ‘under-determined’ and ‘over-determined’ valuations (Dunn), a ‘useful four-valued logic’ (Belnap), and the notion of a bilattice (Ginsberg). We consider within one general framework the notions of constructive truth and constructi...

This paper presents a parameterized reasoning approach with uncertainty based on a lattice-valued logic system. In this uncertain reasoning approach, some parameters are used to represent uncertainty arising from different sources, which is a common phenomenon in rule-based systems. In our system, reasoning with different parameter values means reasoning with different levels of belief and cons...

In his well-known paper \How computer should think" ((Be77b]) Belnap argues that four valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the four-valued structure has among Ginsberg's well-known bilattices is similar to the role that the two-valued algebra has among Boolean algebras. Speciically, w...

Axiomatic bases of admissible rules are obtained for fragments of the substructural logic R-mingle. In particular, it is shown that a “modus-ponens-like” rule introduced by Arnon Avron forms a basis for the admissible rules of its implication and implication-fusion fragments, while a basis for the admissible rules of the full multiplicative fragment requires an additional countably infinite set...