. Two families of many-valued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite many-valued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be many-valued. Gentzen sequent calculi are given for both versions, and soundness and completeness are established. 1 Introduction The logics that have appeared in artificial intelligence form a rich and varied collection. While classical (and maybe intuitionistic) logic su#ces for the formal development of mathematics, artificial intelligence has found uses for modal, temporal, relevant, and many-valued logics, among others. Indeed, I take it as a basic principle that an application should find (or create) an appropriate logic, if it needs one, rather than reshape the application to fit some narrow class of `established' logics. In this paper I want to enlarge the variety of logics...

. Signed formula can be used to reason about a wide variety of multiple-valued logics. The formal theoretical foundation of logic programming based on signed formulas is developed in [26]. In this paper, the operational semantics of signed formula logic programming is investigated through constraint logic programming. Applications to bilattice logic programming and truthmaintenance are considered. Keywords: Logic for Artificial Intelligence, Multiple-valued Logic, Signed Formula, Constraint Logic Programming, Truth-Maintenance, Bilattices * Please address all correspondence to: James Lu Department of Computer Science Bucknell University Lewisburg, PA 17837 U.S.A. E-mail: jameslu@bucknell.edu Phone: +1 717 524 1394 Fax: +1 717 524 1822 ** Work supported in part by the NSF under Grant CCR9225037. SIGNED FORMULA LOGIC PROGRAMMING 1 1. Introduction The logic of signed formulas facilitates the examination of questions regarding multiple-valued logics through classical logic. As...

Integrating knowledge from multiple sources is an important aspect of automated reasoning systems. In [23], we presented a uniform declarative and operational framework, based on annotated logics, for amalgamating multiple knowledge bases and data structures (e.g. relational, object-oriented, spatial, and temporal structures) when these knowledge bases (possibly) contain inconsistencies, uncertainties, and non-monotonic modes of negation. We showed that annotated logics may be used, with some modifications, to mediate between different knowledge bases. The multiple knowledge bases are amalgamated by embedding the individual knowledge bases into a lattice. In this paper, we describe how, given a network of sites where the different databases reside, it is possible to define a distributed semantics for amalgamated knowledge bases. More importantly, we study how the mediator may be distributed across multiple sites so that when certain conditions are satisfied, network failures do not af...