Intensional Part Research Articles

Remarks on the problem of Sense in a pragmatic reading

The division of the problems about Meaning in an extensional and an intensional theory was accused of unnecessarily duplicating the theoretical problems involved in the knowledge of Meaning. The result was either 1. an aggressive rejection of the intensional part of the problem or 2. the adoption of non-classical semantics to account for intensions. This paper suggests a reading of Frege's theory of Meaning that preserves the contribution of the intensional aspect of the question without sacrificing the benefits of the classical insights. For this, however, we need to expand his theory to cases of semantic values which are not directly assertive, that is, what Micheal Dummett called ingredient value. This solution preserves the direct and intuitive insights of classical semantics, expanding it to cases where the designation of truth or falsehood does not have a unified interpretation: speculative, modal, ambiguous, relative cases or cases in which theories disputing Meaning is not straightforwardly mapped to the truth or the not-truth. The paper is a contribution to support the pragmatic interpretation of Frege's legacy by Micheal Dummett.

The intensional side of algebraic-topological representation theorems

Stone representation theorems are a central ingredient in the metatheory of philosophical logics and are used to establish modal embedding results in a general but indirect and non-constructive way. Their use in logical embeddings will be reviewed and it will be shown how they can be circumvented in favour of direct and constructive arguments through the methods of analytic proof theory, and how the intensional part of the representation results can be recovered from the syntactic proof of those embeddings. Analytic methods will also be used to establish the embedding of subintuitionistic logics into the corresponding modal logics. Finally, proof-theoretic embeddings will be interpreted as a reduction of classes of word problems.

Answering Queries Addressed to Several Databases According to a Majority Merging Approach

The general context of this work is the problem of merging data provided by several sources which can be contradictory. Focusing on the case when the information sources do not contain any disjunction, this paper first defines a propositional modal logic for reasoning with data obtained by merging several information sources according to a majority approach. Then it defines a theorem prover to automatically deduce these merged data. Finally, it shows how to use this prover to implement a query evaluator which answers queries addressed to several databases. This evaluator is such that the answer to a query is the one that could be computed by a classical evaluator if the query was addressed to the merged databases. The databases we consider are made of an extensional part, i.e. a set of positive or negative ground literals, and an intensional part i.e. a set of first order function-free clauses. A restriction is imposed to these databases in order to avoid disjunctive data.

Querying several conflicting databases

This paper addresses the problem of querying several databases considered as a whole. Assuming that the different databases share a common data description language, the problem that arises is to consistently answer queries even if the database contents are contradictory. The main contribution of this paper is the specification of a query-evaluator for answering closed and open general queries addressed to several databases and for providing explanations about the results. For doing so, we first specify a query-evaluator, in logic, which assumes that the databases are propositional ones and do not contain disjunctions. Then we extend it to first-order databases defined by an extensional part (sets of positive or negative facts) and an intensional part (sets of first order clauses). We also show that the query-evaluator corresponds to a majority merging of the databases.