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Relational semantics for the 4-valued relevant logics BN4 and E4

100%
Robles G., Blanco J. M., López S. M., Paradela J. R., Recio M. M.
Logic and Logical Philosophy
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2016
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vol. 25
|
issue 2
173-201
EN
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.
2

Relational semantics for the 4-valued relevant logics BN4 and E4

100%
Robles G.
Logic and Logical Philosophy
|
2016
|
vol. 25
|
issue 2
173–201
EN
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.
3

Rational Agency from a Truth-Functional Perspective

100%
Kubyshkina E., Zaitsev D. V.
Logic and Logical Philosophy
|
2016
|
vol. 25
|
issue 4
499-520
EN
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 rational agent, where the fact of knowing something is formalized at the level of valuations, without the explicit use of epistemic knowledge operator. On the basis of this semantics, a sound and complete system with two distinct truth-functional negations (an “ontological” and an “epistemic” one) is provided. These negations allow us to express the statements about knowing or not knowing something at the syntactic level. Moreover, such a system is applied to the analysis of knowability paradox. In particular, we show that the paradox is not derivable in terms of the logic of rational agent.
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