Details

Autor(en) / Beteiligte

• Gemma Robles
• José M. Méndez

Titel

Chapter 6 - Extensions and expansions of the basic logics

Ist Teil von

• Routley-Meyer Ternary Relational Semantics for Intuitionistic-Type Negations, 2018, p.75-107

Ort / Verlag

Elsevier Ltd

Erscheinungsjahr

2018

Link zum Volltext

Quelle

ScienceDirect eBooks

Beschreibungen/Notizen

• In this chapter, we investigate a wealth of extensions and expansions of the basic logics B+, BK+, BcS, BKS, Bc, BK, BcSf, BKSf, Bcf, BKf,RBc, RBc2 and RB+,t,f. These extensions and expansions are defined from the set of schemes t1–t71 that are displayed below. This set contains several well-known theses of propositional logic leaning on which it is shown how to model different kinds of intuitionistic-type negations in RM-semantics. Given that an RM-semantics for an EB+-logic L is provided when L-models together with the notion of L-validity are defined (cf. Definition 1.7), the idea is to give a semantical postulate corresponding to each one of the schemes t1–t71. Then soundness and completeness theorems for extensions and expansions of EB+-logics with any set of these schemes are immediate (cf. Theorems 6.10 and 6.17). Some particular extensions and expansions of the basic logics are briefly treated in the following chapter. Of course, there are many other theses that we have not considered and that could be interpreted in RM-semantics and then used to build extensions and expansions of EB+-logics similarly as t1–t71 are going to be interpreted and used. The work on these possible additional theses is left to the readers of the present book.