MVLPA on Monday, August 21st

Session 1 (11:30‑12:30)

11:30‑12:00

Ajay Mallya (University of Texas at Dallas) Horn-based Multi-Valued Verification Model checking is a widely used technique for verifying complex concurrent syste ms. The models used in classical model checking methods are assumed to be complete a nd consistent. However, a recent body of work has shown that this is not always the case, and multi-valued logics have been proposed to represent such models, spawning an extension of classical model checking, known as, multi-valued model checking. In this paper, we define a multi-valued set based semantics for the multi-valued modal $\mu$-calculus and present a novel interpretation of logic programs to support multi-valued sets as first-class entities, that can be used as a practic al deductive multi-valued model checking framework. This framework provides a semantics preserving encoding of multi-valued transition systems, and allows verification of arbitrary multi-valued modal $\mu$-calculus properties. An implementation of this framework has also been realized.

12:00‑12:30

Zoran Majkic (University of Maryland, College Park) Functional Many-valued Logic and Global Predicate Compression Knowledge-base systems must typically deal with imperfection in knowledge, in particular, in the form of incompleteness and uncertainty. Extensions to many-valued logic programming and deductive databases for handling incompleteness/uncertainty are numerous. They can broadly be characterized into non-probabilistic and probabilistic formalisms. In this paper we show how the higher types of Herbrand interpretations for logic programs, where it is not possible to associate a fixed logic value (a constant from a given domain of truth values) to a given ground atom of a Herbrand base, arise often in practice when we have to deal with uncertain or imprecise information. They arise also in the compression of databases, that is, in a kind of database encapsulation where some number of attributes of its relations are hidden from users. In this paper we present the canonical transformation of standard many-valued logics into functional many-valued logics with higher-order Herbrand interpretation types, and their flattening into 2-valued logics with the ordinary Herbrand interpretations. We show that the global predicate compression and decompression are mutually inverse in the Galois connection. We define the semilattice of higher order Herbrand interpretations and show that they are the result of the application of the observational equivalence to the ordinary Herbrand interpretation semilattice.

Lunch break (12:30‑14:00)

Session 2: Invited Talk (14:00‑15:30)

14:00‑15:00

Michael Gelfond (Texas Tech University) Probabilistic Reasoning with Answer Sets Joint work with Chitta Baral and Nelson Rushton I give an introduction to {\em P-log} - a language for representing logical and probabilistic information in the form of a probabilistic logic program. The semantics of the language associates the program with a set of possible worlds and a measure on them, which can be used to answer queries about the probability of a formula $F$ with respect to the knowledge represented in the program. The logical foundation of our semantics is Answer Set Prolog. Causal Bayesian networks provide the probabilistic foundation. The language and its use for logical and probabilistic reasoning will be illustrated by several examples.

15:00‑15:30

Rajesh Kumar (Carnegie Mellon University) Ashish Tiwari (SRI International) Bruce Krogh (Carnegie Mellon University) EOLC: Efficiently Modelling Inconsistency for Commonsense Reasoning This paper presents EOLC, a declarative logic programming language for commonsense reasoning incorporating non-monotonicity using a four-valued logic, to explicitly model overspecified information, priorities among rules using an overrides predicate, arithmetic constraints, and optimization through an ordering operator `rank'. EOLC also supports the recursive definition of rules. We give the declarative semantics of EOLC and present results about the models of EOLC programs and the complexity of inferencing in EOLC.

Break (15:30‑16:00)

Session 3 (16:00‑17:30)

16:00‑16:30	Ajay Mallya Four-Valued Models and Abstract Game Structures
16:30‑17:00	Alan Bond (UCLA and NIST) A distributed modular logic programming model based on the cortex We developed a distributed modular architecture based on distribution of processing and storage according to data type, inspired by an analysis of the primate cortex. Data items and rules have sets of weights, and these are updated, attenuated and combined in various ways to allow data storage management and rule competition. There are many motivations for using weights, including modeling strengths of different primate behaviors, storage management so that data items are stored and removed from store as needed, rule selection by competition based on computed weight, rule selection stability by confirmation feedback among modules, time smearing to prevent propagation delay problems within the distributed architecture, and the desire to eventually find corresponding neural models.
17:00‑17:30	Andrew Mironov (professor of Moscow State University) Virendra Bhavsar (professor of University of New Brunswick) Fuzzy Modal Logics In the paper we introduce logical calculi for representation of propositions which can contain fuzziness modalities (i.e. modal operators which are indexed by elements of some complete Heyting algebra of fuzziness measures). The proposed calculi are generalizations of propositional modal logics. These calculi are called fuzzy modal logics. We introduce the concept of a fuzzy Kripke model and consider a semantics of fuzzy modal logics at the class of fuzzy Kripke models. The main result of the paper is the completeness theorem of a minimal fuzzy modal logic at the class of fuzzy Kripke models.