Preservation of Craig interpolation by the product of matrix logics

The product of matrix logics, possibly with additional interaction axioms, is shown to preserve a slightly relaxed notion of Craig interpolation. The result is established symbolically, capitalizing on the complete axiomatization of the product of matrix logics provided by their meet-combination. Along the way preservation of the metatheorem of deduction is also proved. The computation of the interpolant in the resulting logic is proved to be polynomially reducible to the computation of the interpolants in the two given logics. Illustrations are provided for classical, intuitionistic and modal propositional logics.     

Judging a book by its cover and its contents: the representation of polysemous and homophonous meanings in four-year-old children

Unlike homophonous meanings, which are semantically unrelated (e.g., the use of bat to refer to a baseball bat and a flying rodent), polysemous meanings are systematically related to one another (e.g., the use of book, CD, and video to refer to physical objects, as in ‘the leather book’, or to the intellectual content they contain, as in ‘the profound book’). But do perceived relations among polysemous meanings reflect the presence of generative lexical or conceptual structures that permit the meanings of these words to shift? If so, these structures may also support children’s early representations of polysemous meanings. In four studies, we demonstrate (1) that four-year-old children can understand both the concrete and abstract meanings of words like book, (2) that when taught a novel label for one of these meanings, children can readily understand an extension of that label to the other meaning, and (3) that extension does not occur between two homophonous meanings, which share a common phonological form but are otherwise unrelated. We conclude that the polysemous meanings of words like book rely on a common representational base early in development, and suggest that this may be the result of foundational, generative properties of the lexicon or conceptual system.     

AN ARCHIMEDEAN POINT FOR PHILOSOPHY

Abstract: According to an orthodox account of meaning and translation, meaning is a property of expressions of a language, and translation is a matching of synonymous expressions across languages. This linguistic account of translation gives rise to well‐known skeptical conclusions about translation, objectivity, meaning, and truth, but it does not conform to our best translational practices. In contrast, I argue for a textual account of meaning based on the concept of a text‐type that does conform to our best translational practices. With their semantic function in view, text‐types are Archimedean points for their respective disciplines. The text‐type of philosophy is no exception. Culture‐transcendent conceptual analysis can proceed on firm footing without having to deny the reality of radical cultural and linguistic difference by treating components of text‐types as the concepts to be analyzed. Analyses of central philosophical concepts are provided as a means of adjudicating philosophical controversy.     

Hybrid logic with the difference modality for generalisations of graphs

We discuss recent work generalising the basic hybrid logic with the difference modality to any reasonable notion of transition. This applies equally to both subrelational transitions such as monotone neighbourhood frames or selection function models as well as those with more structure such as Markov chains and alternating temporal frames. We provide a generic canonical cut-free sequent system and a terminating proof-search strategy for the fragment without the difference modality but including the global modality.     

Modal Platonism: an Easy Way to Avoid Ontological Commitment to Abstract Entities

Modal Platonism utilizes “weak” logical possibility, such that it is logically possible there are abstract entities, and logically possible there are none. Modal Platonism also utilizes a non-indexical actuality operator. Modal Platonism is the EASY WAY, neither reductionist nor eliminativist, but embracing the Platonistic language of abstract entities while eliminating ontological commitment to them. STATEMENT OF MODAL PLATONISM. Any consistent statement B ontologically committed to abstract entities may be replaced by an empirically equivalent modalization, MOD(B), not so ontologically committed. This equivalence is provable using Modal/Actuality Logic S5@. Let MAX be a strong set theory with individuals. Then the following Schematic Bombshell Result (SBR) can be shown: MAX logically yields [T is true if and only if MOD(T) is true], for scientific theories T. The proof utilizes Stephen Neale’s clever model-theoretic interpretation of Quantified Lewis S5, which I extend to S5@.     

A comprehensive semantic framework for data integration systems

A data integration system provides the user with a unified view, called global schema, of the data residing at different sources. Users issue their queries against the global schema, and the system computes answers to queries by suitably accessing the sources, through the mapping, i.e., the specification of the relationship between the global schema and the sources. Since sources are in general autonomous subsystems, the information provided by the data at the sources and the mapping is likely not to be consistent with the knowledge expressed by the global schema. Therefore, the question arises of how to interpret user queries in such a situation, i.e., in the presence of data contradicting the global schema and the mapping. In this paper, we provide an in-depth analysis of the problem of dealing with inconsistencies in data integration systems. In this respect, we highlight the central role played by the mapping, and propose a general “mapping-centered” semantics that allows for computing significant answers to user queries even in the presence of inconsistent information. Based on such a semantic analysis, we define a general formal framework for data integration. Then, we argue that our semantic approach formalizes a very reasonable way of handling inconsistency in such systems, since practically all the existing proposals in the literature can be reconstructed in our framework. This allows for comparing and evaluating the different existing proposals.     

Logic of primary-conditionals and secondary-conditionals

Firstly, the authors analyzed the properties of primary-onditionals and secondary-conditionals, establish the minimum system C2L _m of primary-conditionals and secondary-conditionals, and then prove some of the formal theorems of the system which have important intuitive meanings. Secondly, the authors constructed the neighborhood semantics, prove the soundness of C2L _m, introduce a general concept of canonical model by the neighborhood semantics, and then prove the completeness of C2L _m by the canonical model. Finally, according to the technical results of the minimum system C2L _m, the authors discuss some of the important problems concerning primary-conditionals and secondary-onditionals. __________ Translated from Luoji Yu Renzhi 逻辑与认知 (Logic and Cognition) (online journal), 2004 (3)     

Compositionality and the Prospect of a Pluralistic Semantic Theory

A semantic theory is committed to semantic monism just in case every particular semantic property posited by the theory is a member of the same kind. The commitment to semantic monism appears to draw some support from the need to provide a compositional semantics, since taking a single kind of semantic property as key to a semantic theory affords a uniform pattern on the basis of which the meaning of any given sentence can be compositionally determined. This line of support highlights a tension between the principle of compositionality and taking a more pluralistic approach to semantic theorizing. In this essay, that tension is relieved, leaving open the prospect of a pluralistic semantic theory that observes the principle of compositionality.     

What is <Emphasis Type="Italic">the</Emphasis> Logic of Inference?

The topic of this paper is the question whether there is a logic which could be justly called the logic of inference. It may seem that at least since Prawitz, Dummett and others demonstrated the proof-theoretical prominency of intuitionistic logic, the forthcoming answer is that it is this logic that is the obvious choice for the accolade. Though there is little doubt that this choice is correct (provided that inference is construed as inherently single-conclusion and complying with the Gentzenian structural rules), I do not think that the usual justification of it is satisfactory. Therefore, I will first try to clarify what exactly is meant by the question, and then sketch a conceptual framework in which it can be reasonably handled. I will introduce the concept of ‘inferentially native’ logical operators (those which explicate inferential properties) and I will show that the axiomatization of these operators leads to the axiomatic system of intuitionistic logic. Finally, I will discuss what modifications of this answer enter the picture when more general notions of inference are considered. Presented by Hannes Leitgeb