Some theorems on structural entailment relations

The classesMatr( \( \subseteq \) ) of all matrices (models) for structural finitistic entailments \( \subseteq \) are investigated. The purpose of the paper is to prove three theorems: Theorem I.7, being the counterpart of the main theorem from Czelakowski [3], and Theorems II.2 and III.2 being the entailment counterparts of Bloom's results [1]. Theorem I.7 states that if a classK of matrices is adequate for \( \subseteq \) , thenMatr( \( \subseteq \) ) is the least class of matrices containingK and closed under the formation of ultraproducts, submatrices, strict homomorphisms and strict homomorphic pre-images. Theorem II.2 in Section II gives sufficient and necessary conditions for a structural entailment to be finitistic. Section III contains theorems which characterize finitely based entailments.     

Strong versus weak quantum consequence operations

This paper is a study of similarities and differences between strong and weak quantum consequence operations determined by a given class of ortholattices. We prove that the only strong orthologics which admits the deduction theorem (the only strong orthologics with algebraic semantics, the only equivalential strong orthologics, respectively) is the classical logic.     

Some theorems in haploscopic vision

Three formal hypotheses are specified concerning the combination of neural signals from the two eyes. The hypotheses are (1) that a large uniform light presented to the opposite eye has no effect (independence), (2) that all information from one eye relevant to a given percept (for example, brightness) is encoded by a single neural signal (isolation), and (3) the mutually exclusive and exhaustive alternative to isolation (interaction). Though independence or isolation often has been claimed or simply assumed to hold, these hypotheses imply specific empirical relationships. These relationships are derived for brightness and for equilibrium colors. In addition, one model consistent with the interaction hypothesis is developed. The isolation hypothesis is important for generalizing results from monocular experiments to normal binocular vision. If it is false, monocular results can reflect a combination of one eye's neural signals that never occurs with binocular stimuli.     

Some structural determinants of melody recall

Sophisticated musicians were asked to recall, using musical notation, a set of unfamiliar folk tunes that varied in rhythmic structure and referents of tonality. The results showed that memory was facilitated by tonic triad members marking phrase endings, but only when their presence was highlighted by a corresponding pattern of temporal accents. Conversely, recall significantly declined when tonal information was either absent or obscured by rhythmic structure. Error analyses further revealed that the retention of overall pitch contour and information at phrase ending points varied as a function of these manipulations. The results are discussed in terms of a framework that links the acts of perceiving and remembering to a common attentional scheme.     

Two operations in character recognition: Some evidence from reaction-time measurements

Theories of the recognition of a visual character may be divided into three sets.defined by the way in which the stimulus is encoded before being compared to a memorized target character. A character-classification experiment was performed in which the test stimuli were characters that were either intact or degraded by a superimposed pattern. Analyses of reaction-times in the experiment lead to the rejection of two of the three sets of theories. There appear to be at least two separate operations in the recognition or classification of a character. The first encodes the visual stimulus as an abstracted representation of its physical properties. The second, which may occur more than once, compares such a stimulus representation to a memory representation, producing either a match or a mismatch. A theory of high-speed exhaustive scanning in memory underlies the experiment and is given new support. The method of reaction-time analysis that is introduced, an elaboration of the Uelmholtz-Donders subtraction method, may be applicable to the general problem of the invariance ofperceived form under certain transfomations of the stimulus.     

Two theorems on many-valued logics

This research was supported by the Natural Sciences and Engineering Research Council of Canada under grant A9136.     

Command and consequence

Philosophical Studies - An argument is usually said to be valid iff it is truth-preserving—iff it cannot be that all its premises are true and its conclusion false. But imperatives (it is...     

The strong proof from hypotheses and conditionals: Some theorems of deduction for relevant systems

The aim of this paper is to present a modified version of the notion of strong proof from hypotheses (definition D2), and to give three deduction theorems for the relevant logicsR (theoremsT1, andT2) andE (theoremT3).     

Indirect-deduction theorems

Summary By indirect-deduction theorems introduced in the present paper we mean the theorems that allow to formalize indirect reasonings occurring in deductive practice in general and in mathematics in particular. We discuss the relationship between the introduced theorems and some logical calculi being virtually confined to propositional calculi with implication and negation. It is worth to notice that the above theorems are very handy and effective in proving logical theses.