We observe a number of connections between recent developments in the study of constraint satisfaction problems, irredundant axiomatisation and the study of topological quasivarieties. Several restricted forms of a conjecture of Clark, Davey, Jackson and Pitkethly are solved: for example we show that if, for a finite relational structure M, the class of M-colourable structures has no finite axiomatisation in first order logic, then there is no set (even infinite) of first order sentences characterising the continuously M-colourable structures (...) amongst compact totally disconnected relational structures. We also refute a rather old conjecture of Gorbunov by presenting a finite structure with an infinite irredundant quasi-identity basis. (shrink)

This paper gives a brief survey of current research on the complexity of the constraint satisfaction problem over fixed constraint languages.

In Wason’s Selection Task, subjects: process information from the instructions and build a mental representation of the problem, then: select a course of action to solve the problem,under the constraints imposed by the instructions. We analyze both aspects as part of a constraint satisfaction problem without assuming Wason’s ‘logical’ solution to be the correct one. We show that outcome of step may induce mutually inconsistent constraints, causing subjects to select at step solutions that violate some of them. Our (...) analysis explains why inconsistent constraints are less likely disrupt non-abstract versions of the tasks, but unlike Bayesians does not posit different mechanisms in abstract and thematic variants. We then assess the logicality of the task, and conclude on cognitive tasks as coordination problems. (shrink)

In a seminal 1977 article, Rumelhart argued that perception required the simultaneous use of multiple sources of information, allowing perceivers to optimally interpret sensory information at many levels of representation in real time as information arrives. Building on Rumelhart's arguments, we present the Interactive Activation hypothesis—the idea that the mechanism used in perception and comprehension to achieve these feats exploits an interactive activation process implemented through the bidirectional propagation of activation among simple processing units. We then examine the interactive activation (...) model of letter and word perception and the TRACE model of speech perception, as early attempts to explore this hypothesis, and review the experimental evidence relevant to their assumptions and predictions. We consider how well these models address the computational challenge posed by the problem of perception, and we consider how consistent they are with evidence from behavioral experiments. We examine empirical and theoretical controversies surrounding the idea of interactive processing, including a controversy that swirls around the relationship between interactive computation and optimal Bayesian inference. Some of the implementation details of early versions of interactive activation models caused deviation from optimality and from aspects of human performance data. More recent versions of these models, however, overcome these deficiencies. Among these is a model called the multinomial interactive activation model, which explicitly links interactive activation and Bayesian computations. We also review evidence from neurophysiological and neuroimaging studies supporting the view that interactive processing is a characteristic of the perceptual processing machinery in the brain. In sum, we argue that a computational analysis, as well as behavioral and neuroscience evidence, all support the Interactive Activation hypothesis. The evidence suggests that contemporary versions of models based on the idea of interactive activation continue to provide a basis for efforts to achieve a fuller understanding of the process of perception. (shrink)

We investigate the complexity of finding solutions to infinite recursive constraint satisfaction problems. We show that, in general, the problem of finding a solution to an infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through a recursive tree. We also identify natural classes of infinite recursive constraint satisfaction problems where the problem of finding a solution to the infinite recursive constraint satisfaction problem is equivalent to (...) the problem of finding an infinite path through finitely branching recursive trees or recursive binary trees. There are a large number of results in the literature on the complexity of the problem of finding an infinite path through a recursive tree. Our main result allows us to automatically transfer such results to give equivalent results about the complexity of the problem of finding a solution to a recursive constraint satisfaction problem. (shrink)

A pioneering look at the fundamental role of logic in optimizationand constraint satisfaction While recent efforts to combine optimization and constraintsatisfaction have received considerable attention, little has beensaid about using logic in optimization as the key to unifying thetwo fields. Logic-Based Methods for Optimization develops for thefirst time a comprehensive conceptual framework for integratingoptimization and constraint satisfaction, then goes a step furtherand shows how extending logical inference to optimization allowsfor more powerful as well as flexible modeling (...) and solutiontechniques. Designed to be easily accessible to industryprofessionals and academics in both operations research andartificial intelligence, the book provides a wealth of examples aswell as elegant techniques and modeling frameworks ready forimplementation. Timely, original, and thought-provoking,Logic-Based Methods for Optimization: * Demonstrates the advantages of combining the techniques inproblem solving * Offers tutorials in constraint satisfaction/constraintprogramming and logical inference * Clearly explains such concepts as relaxation, cutting planes,nonserial dynamic programming, and Bender's decomposition * Reviews the necessary technologies for software developersseeking to combine the two techniques * Features extensive references to important computationalstudies * And much more. (shrink)

There exist two conjectures for constraint satisfaction problems of reducts of finitely bounded homogeneous structures: the first one states that tractability of the CSP of such a structure is, when the structure is a model-complete core, equivalent to its polymorphism clone satisfying a certain nontrivial linear identity modulo outer embeddings. The second conjecture, challenging the approach via model-complete cores by reflections, states that tractability is equivalent to the linear identities satisfied by its polymorphisms clone, together with the natural (...) uniformity on it, being nontrivial. We prove that the identities satisfied in the polymorphism clone of a structure allow for conclusions about the orbit growth of its automorphism group, and apply this to show that the two conjectures are equivalent. We contrast this with a counterexample showing that [Formula: see text]-categoricity alone is insufficient to imply the equivalence of the two conditions above in a model-complete core. Taking another approach, we then show how the Ramsey property of a homogeneous structure can be utilized for obtaining a similar equivalence under different conditions. We then prove that any polymorphism of sufficiently large arity which is totally symmetric modulo outer embeddings of a finitely bounded structure can be turned into a nontrivial system of linear identities, and obtain nontrivial linear identities for all tractable cases of reducts of the rational order, the random graph, and the random poset. Finally, we provide a new and short proof, in the language of monoids, of the theorem stating that every [Formula: see text]-categorical structure is homomorphically equivalent to a model-complete core. (shrink)