Results 1  10
of
25
The Origin of Relation Algebras in the Development and Axiomatization of the Calculus of Relations
, 1991
"... ..."
Logic, Optimization, and Constraint Programming
 INFORMS Journal on Computing
, 2000
"... Because of their complementary strengths, optimization and constraint programming can be profitably merged. Their integration has been the subject of increasing commercial and research activity. This paper summarizes and contrasts the characteristics of the two fields; in particular, how they use ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
Because of their complementary strengths, optimization and constraint programming can be profitably merged. Their integration has been the subject of increasing commercial and research activity. This paper summarizes and contrasts the characteristics of the two fields; in particular, how they use logical inference in di#erent ways, and how these ways can be combined. It sketches the intellectual background for recent e#orts at integration. In particular, it traces the history of logicbased methods in optimization and the development of constraint programming in artificial intelligence. It concludes with a review of recent research, with emphasis on schemes for integration, relaxation methods, and practical applications. Optimization and constraint programming are beginning to converge, despite their very di#erent origins. Optimization is primarily associated with mathematics and engineering, while constraint programming developed much more recently in the computer science an...
RelationAlgebraic Semantics
 Theoretical Computer Science
, 1996
"... The first half is a tutorial on orderings, lattices, Boolean algebras, operators on Boolean algebras, Tarski's fixed point theorem, and relation algebras. ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
The first half is a tutorial on orderings, lattices, Boolean algebras, operators on Boolean algebras, Tarski's fixed point theorem, and relation algebras.
On the Complexity of Boolean Unification
 INFORMATION PROCESSING LETTERS
, 1997
"... Unification modulo the theory of Boolean algebras has been investigated by several autors. Nevertheless, the exact complexity of the decision problem for unification with constants and general unification was not known. In this research note, we show that the decision problem is \Pi p 2  complete ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
Unification modulo the theory of Boolean algebras has been investigated by several autors. Nevertheless, the exact complexity of the decision problem for unification with constants and general unification was not known. In this research note, we show that the decision problem is \Pi p 2  complete for unification with constants and PSPACEcomplete for general unification. In contrast, the decision problem for elementary unification (where the terms to be unified contain only symbols of the signature of Boolean algebras) is "only" NPcomplete.
NonBoolean Descriptions for MindMatter Problems
"... A framework for the mindmatter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive nonBoolean description of a world without an apriorigiven mindmat ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
A framework for the mindmatter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive nonBoolean description of a world without an apriorigiven mindmatter distinction. Such a description in terms of a locally Boolean but globally nonBoolean structure makes allowance for the fact that Boolean descriptions play a privileged role in science. If we accept the insight that there are no ultimate building blocks, the existence of holistic correlations between contextually chosen parts is a natural consequence. The main problem of a genuinely nonBoolean description is to find an appropriate partition of the universe of discourse. If we adopt the idea that all fundamental laws of physics are invariant under time translations, then we can consider a partition of the world into a tenseless and a tensed domain. In the sense of a regulative principle, the material domain is defined as the tenseless domain with its homogeneous time. The tensed domain contains the mental domain with a tensed time characterized by a privileged position, the Now. Since this partition refers to two complementary descriptions which are not given apriori,wehavetoexpectcorrelations between these two domains. In physics it corresponds to Newton’s separation of universal laws of nature and contingent initial conditions. Both descriptions have a nonBoolean structure and can be encompassed into a single nonBoolean description. Tensed and tenseless time can be synchronized by holistic correlations. 1.
Traditional logic, modern logic and natural language
"... DRAFT June 2009. The paper is for a Festschrift and this draft has removed a number of personal references. 1 The questions... Wikipedia [38] defines: traditional logic is ‘a loose name for the way of doing logic that began with Aristotle, and that was dominant until the advent of modern predicate l ..."
Abstract

Cited by 6 (6 self)
 Add to MetaCart
DRAFT June 2009. The paper is for a Festschrift and this draft has removed a number of personal references. 1 The questions... Wikipedia [38] defines: traditional logic is ‘a loose name for the way of doing logic that began with Aristotle, and that was dominant until the advent of modern predicate logic in the late nineteenth century’. It is of great interest to place the transitions between traditional and modern logic. In this paper I will say where I think the main differences lie. In my last section I will comment on... the relationship between some traditional argument forms and natural language argument. The strength of traditional logic is sometimes measured in terms of the valid inference patterns that it recognises. Among other patterns: (1) “Some P R all Q ” implies “All Q are Red by some P ”. and the pattern behind some inferences that De Morgan studied: (2) “All horses are animals. So, all horse tails are animal tails.”. This is not a new measure; it was widely used in the mid 20th century
Modelling Social Interaction Attitudes in MultiAgent Systems
, 2001
"... Abstract 2 Most autonomous agents are situated in a social context and need to interact with other agents (both human and artificial) to complete their problem solving objectives. Such agents are usually capable of performing a wide range of actions and engaging in a variety of social interactions. ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
Abstract 2 Most autonomous agents are situated in a social context and need to interact with other agents (both human and artificial) to complete their problem solving objectives. Such agents are usually capable of performing a wide range of actions and engaging in a variety of social interactions. Faced with this variety of options, an agent must decide what to do. There are many potential decision making functions that could be employed to make the choice. Each such function will have a different effect on the success of the individual agent and of the overall system in which it is situated. To this end, this thesis examines agents ’ decision making functions to ascertain their likely properties and attributes. A novel framework for characterising social decision making is presented which provides explicit reasoning about the potential benefits of the individual agent, particular subgroups of agents or the overall system. This framework enables multifarious social interaction attitudes to be identified and defined; ranging from the purely selfinterested to the purely altruistic. In particular, however, the focus is on the spectrum of socially responsible agent behaviours in which agents attempt to balance their own needs with those of the overall system. Such behaviour aims to ensure that both the agent and the overall system perform well.
Relation algebras for reasoning about time and space
 Algebraic Methodology and Software Technology, Enschede 1993, Workshops in Computing Series
, 1994
"... This paper presents a brief introduction to relation algebras, including some examples motivated by work in computer science, namely, the ‘interval algebras’, relation algebras that arose from James Allen’s work on temporal reasoning, and by ‘compass algebras’, which are designed for similar reasoni ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
This paper presents a brief introduction to relation algebras, including some examples motivated by work in computer science, namely, the ‘interval algebras’, relation algebras that arose from James Allen’s work on temporal reasoning, and by ‘compass algebras’, which are designed for similar reasoning about space. One kind of reasoning problem, called a ‘constraint satisfaction problem’, can be defined for arbitrary relation algebras. It will be shown here that the constraint satisfiability problem is NPcomplete for almost all compass and interval algebras.
Algebraic Terminological Representation
, 1991
"... This thesis investigates terminological representation languages, as used in klonetype knowledge representation systems, from an algebraic point of view. Terminological representation languages are based on two primitive syntactic types, called concepts and roles, which are usually interpreted mo ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
This thesis investigates terminological representation languages, as used in klonetype knowledge representation systems, from an algebraic point of view. Terminological representation languages are based on two primitive syntactic types, called concepts and roles, which are usually interpreted modeltheoretically as sets and relations, respectively. I propose an algebraic rather than a modeltheoretic approach. I show that terminological representations can be naturally accommodated in equational algebras of sets interacting with relations, and I use equational logic as a vehicle for reasoning about concepts interacting with roles.
The Logic of Quantum Physics
 Transactions of the New York Academy of Science
, 1963
"... We present the principles of classical and quantum logic in comparable operational ways. The classical system has an absolute state., but the quantum one has states relative to an operational frame. This relativism conflicts with the usual implications of the term “real; ” a term like “actual ” or ‘ ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We present the principles of classical and quantum logic in comparable operational ways. The classical system has an absolute state., but the quantum one has states relative to an operational frame. This relativism conflicts with the usual implications of the term “real; ” a term like “actual ” or ‘operational ” is more appropriate for what quantum theory describes. The duality between epistemical and dynamical processes is the same for classical and quantum physics; there is no problem of measurement peculiar to quantum theory. 1 Philosophical introduction Boole may have been the first to formulate logic in an operational way, and on the same page he declared that it was empirical and hence doubtable. Many people who make an issue of reality in discussions of quantum theory are not conscious of a deeply entrenched axiom that reality is subject to Boolean logic, and so are not prepared to doubt this axiom. “Reality ” in the absolute sense is an idol in the sense of Francis Bacon, and an idol of the theater, tribe, and cave all at once. Quantum theory denies the existence of an absolute reality. Heisenberg, Bohr, and Von Neumann were also prepared to doubt the applicability of Boolean logic to nature. Von Neumann