The experimental logic of Moore and Mealy type automata is investigated. key words: automaton logic; partition logic; comparison to quantum logic; intrinsic measurements 1

A lattice theoretic framework for the calculus of program refinement is presented. Specifications and program statements are combined into a single (infinitary) language of commands which permits miraculous, angelic and demonic statements to be used in the description of program behavior. The weakest precondition calculus is extended to cover this larger class of statements and a game-theoretic interpretation is given for these constructs. The language is complete, in the sense that every monotonic predicate transformer can be expressed in it. The usual program constructs can be defined as derived notions in this language. The notion of inverse statements is defined and its use in formalizing the notion of data refinement is shown.

This paper describes a uniform formalization of much of the current work in AI on inference systems. We show that many of these systems, including first-order theorem provers, assumption-based truth maintenance systems (atms's) and unimplemented formal systems such as default logic or circumscription can be subsumed under a single general framework. We begin by defining this framework, which is based on a mathematical structure known as a bilattice. We present a formal definition of inference using this structure, and show that this definition generalizes work involving atms's and some simple nonmonotonic logics. Following the theoretical description, we describe a constructive approach to inference in this setting; the resulting generalization of both conventional inference and atms's is achieved without incurring any substantial computational overhead. We show that our approach can also be used to implement a default reasoner, and discuss a combination of default and atms methods th...

The Region-Connection Calculus (RCC) is a well established formal system for qualitative spatial reasoning. It provides an axiomatization of space which takes regions as primitive, rather than as constructions from sets of points. The paper introduces boolean connection algebras (BCAs), and proves that these structures are equivalent to models of the RCC axioms. BCAs permit a wealth of results from the theory of lattices and boolean algebras to be applied to RCC. This is demonstrated by two theorems which provide constructions for BCAs from suitable distributive lattices. It is already well known that regular connected topological spaces yield models of RCC, but the theorems in this paper substantially generalize this result. Additionally, the lattice theoretic techniques used provide the first proof of this result which does not depend on the existence of points in regions. Keywords: Region-Connection Calculus, Qualitative Spatial Reasoning, Boolean Connection Algebra, Mer...

Reduced product of abstract domains is a rather well-known operation for domain composition in abstract interpretation. In this article, we study its inverse operation, introducing a notion of domain complementation in abstract interpretation. Complementation provides a systematic way to design new abstract domains, and it allows to systematically decompose domains. Also, such an operation allows to simplify domain veri cation problems, and it yields space-saving representations for complex domains. We show that the complement exists in most cases, and we apply complementation to three well-known abstract domains, notably to Cousot and Cousot's interval domain for integer variable analysis, to Cousot and Cousot's domain for comportment analysis of functional languages, and to the domain Sharing for aliasing analysis of logic languages.

This paper investigates the problems arising in the construction of a program to play the

Suppose that is a set of problems and is a set of skills. A skill function assigns to each problem -- i.e. to each element of -- those sets of skills which are minimally sufficient to solve ; a problem function assigns to each set X of skills the set of problems which can be solved with these skills (a knowledge state). We explore the natural properties of such functions and show that these concepts are basically the same. Furthermore, we show that for every family of subsets of Q which includes the empty set and , there are a set of (abstract) skills and a problem function whose range is just . We also give a bound for the number of skills needed to generate a specific set of knowledge states, and discuss various ways to supply a set of knowledge states with an underlying skill theory. Finally, a procedure is described to determine a skill function using coverings in partial orders which is applied to set A of the Coloured Progressive Matrices test Raven (1965).

A lattice theoretic approach is developed to study the properties of functional dependencies in relational databases. The particular attention is paid to the analysis of the semilattice of closed sets, the lattice of all closure operations on a given set and to a new characterization of normal form relation schemes. Relation schemes with restrictions on functional dependencies are also studied. 1. Introduction The relational datamodel was defined by E.F. Codd [14] in 1970, and it is still one of the most powerful database models. In this model a relation is a matrix (table) every row of which corresponds to a record and every column to an attribute. This model has been widely studied. One of the most important branches in the theory of relational databases is that dealing with the design of database schemes. This branch is based on the theory of dependencies and constraints. In this paper we study the functional dependencies. Informally, functional dependency means that some attribu...

Closure spaces have been previously investigated by Paul Edelman and Robert Jamison as "convex geometries". Consequently, a number of the results given here duplicate theirs. However, we employ a slightly different, but equivalent, defining axiom which gives a new flavor to our presentation. The major contribution is the definition of a partial order on all subsets, not just closed (or convex) subsets. It is shown that the subsets of a closure space, so ordered, form a lattice with regular, though non-modular, properties. Investigation of this lattice becomes our primary focus. 1 Introduction We let U denote some universe of interest, that is a set of elements, points, or phenomena. Individual points of U will be denoted by lower case letters: a; b; :::; p; q; ::: 2 U. Elements of the power set, 2 U , we will denote by upper case letters: :::; X; Y; Z ` U (or 2 2 U ). Our goal will be to partially order these power set elements. A straightforward partial order by inclusio...

We present an in-depth theoretical, algorithmic and computational study of a linear programming (LP) relaxation to the precedence constrained single machine scheduling problem 1 | prec | sum(w_jC_j) to minimize a weighted sum of job completion times. On the theoretical side, we study the structure of tight parallel inequalities in the LP relaxation and show that every permutation schedule which is consistent with Sidney's decomposition has total cost no more than twice the optimum. On the algorithmic side, we provide a parametric extension to Sidney's decomposition and show that a finest decomposition can be obtained by essentially solving a parametric minimum cut problem. Finally, we report results obtained by an algorithm based on these developments on randomly generated instances with up to 2,000 jobs.