Martin's Axiom,Omitting Types,and Complete Representations in Algebraic Logic

We give a new characterization of the class of completely representable cylindric algebras of dimension 2 #lt; n w via special neat embeddings. We prove an independence result connecting cylindric algebra to Martin's axiom. Finally we apply our results to finite-variable first order logic showing that Henkin and Orey's omitting types theorem fails for L _n, the first order logic restricted to the first n variables when 2 #lt; n#lt;w. L _n has been recently (and quite extensively) studied as a many-dimensional modal logic.     

Varieties of Pseudo-Interior Algebras

The notion of a pseudo-interior algebra was introduced by Blok and Pigozzi in [BPIV]. We continue here our studies begun in [BK]. As a consequence of the representation theorem for pseudo-interior algebras given in [BK] we prove that the variety of all pseudo-interior algebras is generated by its finite members. This result together with Jónsson's Theorem for congruence distributive varieties provides a useful technique in the study of the lattice of varieties of pseudo-interior algebras.     

The Basic Algebra of Game Equivalences

We give a complete axiomatization of the identities of the basic game algebra valid with respect to the abstract game board semantics. We also show that the additional conditions of termination and determinacy of game boards do not introduce new valid identities.En route we introduce a simple translation of game terms into plain modal logic and thus translate, while preserving validity both ways, game identities into modal formulae.The completeness proof is based on reduction of game terms to a certain minimal canonical form, by using only the axiomatic identities, and on showing that the equivalence of two minimal canonical terms can be established from these identities.     

A Coalgebraic View of Heyting Duality

We give a coalgebraic view of the restricted Priestley duality between Heyting algebras and Heyting spaces. More precisely, we show that the category of Heyting spaces is isomorphic to a full subcategory of the category of all -coalgebras, based on Boolean spaces, where is the functor which maps a Boolean space to its hyperspace of nonempty closed subsets. As an appendix, we include a proof of the characterization of Heyting spaces and the morphisms between them.     

On subdirectly irreducible OMAs

In this paper some properties of epi-representations and Schmidt-congruence relations of orthomodular partial algebras are investigated and an infinite list of OMA-epi-subdirectly irreducible orthomodular partial algebras will be constructed.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko     

A Generalization of the Łukasiewicz Algebras

We introduce the variety _n ^m , m 1 and n 2, of m-generalized ukasiewicz algebras of order n and characterize its subdirectly irreducible algebras. The variety _n ^m is semisimple, locally finite and has equationally definable principal congruences. Furthermore, the variety _n ^m contains the variety of ukasiewicz algebras of order n.     

Intuitive physics and cognitive algebra: A review

IntroductionIntuitive physics explores how people without a formal instruction in physics intuitively understand physical phenomena. After a general overview of the topics of current research in intuitive physics and a discussion of current debates, this paper provides an introduction to Information Integration Theory (IIT).ObjectiveBy means of examples, it is shown how IIT can be used to directly compare the algebraic structure of physical laws and the algebraic structure of cognitive representations of these laws.MethodThe review considers about 40 years of research on the application of IIT in the field of intuitive physics. Occasionally, reference is also made to intuitive physics studies outside this theoretical framework.ResultsThe reviewed studies highlight four main factors that affect the degree of consistency between physical laws and cognitive algebraic laws: the participants’ age, their familiarity with the event under study, the type of task, and possible learning processes.ConclusionThe last part of the article discusses the implications of the results of the reviewed studies for the two main current hypotheses on the nature of intuitive physics, namely, that intuitive physics may be based on sub-optimal heuristics or may be based on the internalization of physical laws.     

Notes on Logics of Metric Spaces

In [14], we studied the computational behaviour of various first-order and modal languages interpreted in metric or weaker distance spaces. [13] gave an axiomatisation of an expressive and decidable metric logic. The main result of this paper is in showing that the technique of representing metric spaces by means of Kripke frames can be extended to cover the modal (hybrid) language that is expressively complete over metric spaces for the (undecidable) two-variable fragment of first-order logic with binary pred-icates interpreting the metric. The frame conditions needed correspond rather directly with a Boolean modal logic that is, again, of the same expressivity as the two-variable fragment. We use this representation to derive an axiomatisation of the modal hybrid variant of the two-variable fragment, discuss the compactness property in distance logics, and derive some results on (the failure of) interpolation in distance logics of various expressive power. Presented by Melvin Fitting     

Phonological coding in reading comprehension: The importance of individual differences

Abstract

In two experiments, texts were presented word by word at a fixed pace to subjects high or low in test anxiety, under various concurrent interference conditions: no interference, articulatory suppression, finger tapping, unattended meaningful speech, reversed (meaningless) speech and nonword (meaningless) speech. High-anxiety subjects produced overt articulation more frequently than low-anxiety subjects, especially in the speech conditions. There was an interaction between anxiety and interference on comprehension performance: Conditions thought to interfere with phonological coding (i.e. articulatory suppression and nonword speech) were detrimental to comprehension for high but not for low-anxiety subjects; in contrast, there were no differences in comprehension performance as a function of anxiety under conditions causing no (proper) phonological interference (i.e. no interference, finger tapping and reversed speech). There were mixed results in the meaningful speech condition, partly attributable to its semantic interference component. These findings reveal that the use and importance of phonological coding in reading comprehension vary with differences in test anxiety-high-anxiety subjects are vulnerable to disruptive effects on phonological coding. This suggests that high-anxiety individuals are especially likely to resort to speech-based coding during reading, and that phonological coding has a compensatory role for them.