Relational semantics for the 4-valued relevant logics BN4 and E4
Journal Title: Logic and Logical Philosophy - Year 2016, Vol 25, Issue 2
Abstract
The logic BN4 was defined by R.T. Brady in 1982. It can be considered as the 4-valued logic of the relevant conditional. E4 is a variant of BN4 that can be considered as the 4-valued logic of (relevant) entailment. The aim of this paper is to define reduced general Routley-Meyer semantics for BN4 and E4. It is proved that BN4 and E4 are strongly sound and complete w.r.t. their respective semantics.
Authors and Affiliations
Gemma Robles, José M. Blanco, Sandra M. López, Jesús R. Paradela, Marcos M. Recio
Keywords
Related Articles
- EP ID EP201831
- DOI 10.12775/LLP.2016.006
- Views 77
- Downloads 0
Refutation Systems for a System of Nonsense-Logic
In the paper rejection systems for a system of nonsense-logic are investigated. The first rejection system consists of four rejected axioms and only one rejection rule - the rule of rejection by detachment. The second o...
Interplays of knowledge and non-contingency
This paper combines a non-contingency logic with an epistemic logic by means of fusions and products of modal systems. Some consequences of these interplays are pointed out.
Rational Agency from a Truth-Functional Perspective
The aim of the present paper is to introduce a system, where the epistemic state of an agent is represented truth-functionally. In order to obtain this system, we propose a four-valued logic, that we call the logic of ra...
Category Free Category Theory and Its Philosophical Implications
There exists a dispute in philosophy, going back at least to Leibniz, whether is it possible to view the world as a network of relations and relations between relations with the role of objects, between which these relat...
On some extensions of the class of MV-algebras
In the present paper we will ask for the lattice L(MVEx) of subvarieties of the variety defined by the set Ex(MV) of all externally compatible identities valid in the variety MV of all MV-algebras. In particular, we will...