Marie Duží

Procedural Semantics for Hyperintensional Logic

The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals with all kinds of linguistic context in a fully compositional and anti-contextual way.

Transparent quantification into hyperintensional objectual attitudes

We demonstrate how to validly quantify into hyperintensional contexts involving non-propositional attitudes like seeking, solving, calculating, worshipping, and wanting to become. We describe and apply a typed extensional logic of hyperintensions that preserves compositionality of meaning, referential transparency and substitutivity of identicals also in hyperintensional attitude contexts. We specify and prove rules for quantifying into hyperintensional contexts. These rules presuppose a rigorous method for substituting variables into hyperintensional contexts, and the method will be described. We prove the following. First, it is always valid to quantify into hyperintensional attitude contexts and over hyperintensional entities. Second, factive empirical attitudes (e.g. finding the site of Troy) validate, furthermore, quantifying over intensions and extensions, and so do non-factive attitudes, both empirical and non-empirical (e.g. calculating the last decimal of the expansion of

‘Parmenides principle’ (The analysis of aboutness)

\pi

Knowledge Modeling, Management and Utilization towards Next Generation Web

π), provided the entity to be quantified over exists. We focus mainly on mathematical attitudes, because they are uncontroversially hyperintensional.

Can concepts be defined in terms of sets

This article solves, in a logically rigorous manner, a problem originally advanced as a counterexample to Chomsky’s theory of binding and recently discussed in a 2004 paper by Stephen Neale. The example is this. John loves his wife, and so does Peter. Hence John and Peter share a property. But which one? (i) Loving John’s wife: then John and Peter love the same woman. (ii) Loving one’s own wife: then, unless they are married to the same woman, John loves one woman and Peter loves another woman. Since ‘John loves his wife’ is ambiguous between attributing (i) or (ii) to John, ‘So does Peter’ is also ambiguous between attributing (i) or (ii) to Peter. With unrestricted β-reduction, the lambda-term counterparts of the attributions of (i) and (ii) to John both β-reduce to (ii). Which, intuitively, they should not. With suitably restricted β-conversion, the two redexes do not reduce to the same contractum and can be reconstructed from their respective contracta. This article details how to apply this restricted rule of β-conversion to contexts containing anaphora such as ‘his’ and ‘so does’. The logical contribution of the article is a generally valid form of β-conversion ‘by value’ rather than ‘by name’. The philosophical application of β-conversion ‘by value’ to a context containing anaphora is another contribution of this article.

Iterated privation and positive predication

A explication of aboutness (principle of subject matter) within transparent intensional logic.

How to Unify Russellian and Strawsonian Definite Descriptions

In this paper I describe an extensional logic of hyperintensions, viz. Tichýs Transparent Intensional Logic (TIL). TIL preserves transparency and compositionality in all kinds of context, and validates quantifying into all contexts, including intensional and hyperintensional ones. The availability of an extensional logic of hyperintensions defies the received view that an intensional (let alone hyperintensional) logic is one that fails to validate transparency, compositionality, and quantifying-in. The main features of our logic are that the senses and denotations of (non-indexical) terms and expressions remain invariant across contexts and that our ramified type theory enables quantification over any logical objects of any order. The syntax of TIL is the typed lambda calculus; its semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The only two non-standard features are a hyperintension (called Trivialization) that presents other hyperintensions and a four-place substitution function (called Sub) defined over hyperintensions.

E-Learning Support for Logic Education

Nowadays, large amounts of Web contents are being distributed on the Internet. Conventional search engines are not useful for analyzing the relations between related knowledge since a number of Web contents may indicate a similar concept by different words. Users search Web pages for different purposes, such as for education, for accessing information on current affairs, or for gaining knowledge.We believe that the next-generation Web connects each page with not only conventional hyper links but also knowledge links. The knowledge link has to be created by novel knowledge processing technologies. The technologies consist of knowledge gathering, storage, and delivery technologies. In this study, we discuss novel knowledge modeling, management, distribution, and analysis technologies. All these technologies are essential to build the next-generation Web, named Knowledge Web.