A type-free Gödel interpretation

Canonicity and normalization for dependent type theory

Cartesian closed Dialectica categories

Traditional accounts of the semantic interpretation of quantified phrases and its interaction with reference and ellipsis have relied on formal manipulations of logical forms (quantifier raising) or complicated denotations for phrases (Cooper storage). These complications are one of the motivations for the development of categorial semantic theories. However, these theories appear to face their own difficulties in accounting for the full range of scoping possibilities in natural language, and have been losing some of their original elegance. Experiments suggest that the insights of the traditional theories may be revived in a semantically more respectable form by taking advantage of the abstraction mechanisms of higher-order hereditary Harrop formulae, as implemented in λProlog, to represent scoping and extraction dependencies without the need for formal conditions on logical forms or elaborate denotations for phrases. The technique used is an adaptation of a method of Felty and Miller for dispensing with side conditions in sequent-calculus rules. Finally, it will be seen that this approach is after all a close relative of categorial semantics.

Role of Serum Interleukin-10 Levels in Patients with Chronic Hepatitis B Virus Infection from India

Affective meanings of colors and forms were studied with the Semantic Differential technique and word-color/word-form associations. Results of word-color associations and word-form associations were in close relation with similarities of affective meanings between words and colors and between words and forms. Cross-cultural comparisons indicated wide generality of affective and symbolic meanings of colors and forms. However, some cultural differences were found, especially in evaluation. Affective meanings of various color-combinations and colored forms were compared with those of component colors and forms. Weighted linear combinations of affective effects of component colors or forms were found in those of color-combinations and color-form combinations, but interaction between components were found important especially in the evaluative dimension.

A natural way to represent beliefs and the process of updating beliefs is presented by Bayesian probability theory, where belief of an agent a in P can be interpreted as a considering that P is more probable than not P. This paper attempts to get at the core logical notion underlying this. The paper presents a sound and complete neighbourhood logic for conditional belief and knowledge, and traces the connections with probabilistic logics of belief and knowledge. The key notion in this paper is that of an agent a believing P conditionally on having information Q, where it is assumed that Q is compatible with what a knows. Conditional neighbourhood logic can be viewed as a core system for reasoning about subjective plausibility that is not yet committed to an interpretation in terms of numerical probability. Indeed, every weighted Kripke model gives rise to a conditional neighbourhood model, but not vice versa. We show that our calculus for conditional neighbourhood logic is sound but not complete for weighted Kripke models. Next, we show how to extend the calculus to get completeness for the class of weighted Kripke models. Neighbourhood models for conditional belief are closed under model restriction (public announcement update), while earlier neighbourhood models for belief as `willingness to bet' were not. Therefore the logic we present improves on earlier neighbourhood logics for belief and knowledge. We present complete calculi for public announcement and for publicly revealing the truth value of propositions using reduction axioms. The reductions show that adding these announcement operators to the language does not increase expressive power.

This work introduces the theory of illative combinatory algebras, which is closely related to systems of illative combinatory logic. We thus provide a semantic interpretation for a formal framework in which both logic and computation may be expressed in a unified manner. Systems of illative combinatory logic consist of combinatory logic extended with constants and rules of inference intended to capture logical notions. Our theory does not correspond strictly to any traditional system, but draws inspiration from many. It differs from them in that it couples the notion of truth with the notion of equality between terms, which enables the use of logical formulas in conditional expressions. We give a consistency proof for first-order illative combinatory algebras. A complete embedding of classical predicate logic into our theory is also provided. The translation is very direct and natural.