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Erschienen in:
Basic Postulates for Inconsistency Measures Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

A Proximity-Based Understanding of Conditionals

verfasst von : Ricardo Queiroz de Araujo Fernandes, Edward Hermann Haeusler, Luiz Carlos Pinheiro Dias Pereira

Erschienen in: Transactions on Large-Scale Data- and Knowledge-Centered Systems XXXIV

Verlag: Springer Berlin Heidelberg

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Abstract

The aim of the present paper is to introduce a new logic, PUC-Logic, which will be used to give a systematic account of well-known counterfactuals conditionals on the basis of a concept of proximity. We will formulate a natural deduction system for PUC-Logic, the system PUC-ND, that will be shown to be sound and complete with respect to the semantics of PUC-Logic. We shall also prove that PUC-Logic is decidable and that the system PUC-ND satisfies the normalization theorem.

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Vorheriges Kapitel Formalizing a Paraconsistent Logic in the Isabelle Proof Assistant
Nächstes Kapitel Inconsistency-Tolerant Database Repairs and Simplified Repair Checking by Measure-Based Integrity Checking
Fußnoten
1
The expression state-of-affairs is here used in an intuititive and very general sense as a kind of “truth-maker”, as that piece of reality that is responsible for the truth of a proposition (as Michael Dummett [16] would put it). There’s a long and important discussion in Philosophy as to the true nature of state-of-affairs, but to get into this discussion is clearly beyond the scope of the presente paper.
 
2
\(\$_{i}\) gives the neighborhoods around the world i. They are the available strictness to evaluate counterfactuals at i.
 
3
A \(\phi \)-world is a world in which \(\phi \) holds.
 
4
The notion of closeness or proximity is based on the work of Lewis; it is a topological notion explained in the end of Sect. 2 and formally defined in Sect. 4.
 
5
This definition of database which includes a first-order model B and not only the integrity constraints is similar to the definition of a relational database in [17].
 
6
\(\alpha (b_1,\ldots ,b_n)\) is an abuse of notation; it means that \(b_i\) is assigned to \(x_i\) by means of some assignment function.
 
7
We are going to use labels in the spirit of labelled deductive systems, as it is used by Gabbay and Negri. Labels help us to push down semantic notions into the syntax (see, for example, [22]).
 
8
We use the term wff to denote both the singular and the plural form of the expression well-formed formula.
 
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Metadaten
Titel
A Proximity-Based Understanding of Conditionals
verfasst von
Ricardo Queiroz de Araujo Fernandes
Edward Hermann Haeusler
Luiz Carlos Pinheiro Dias Pereira
Copyright-Jahr
2017
Verlag
Springer Berlin Heidelberg
Buch
Transactions on Large-Scale Data- and Knowledge-Centered Systems XXXIV

Print ISBN: 978-3-662-55946-8

Electronic ISBN: 978-3-662-55947-5

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-662-55947-5_6