This paper discusses three relevant logics (S^fde; dS^ fde; crossS^fde) that obey Component Homogeneity|a principle that Goddard and Routley  introduce in their project of a logic of significance. The paper establishes two main results. First, it establishes a general characterization result for two families of logic that obey Component Homogeneity|that is, we provide a set of necessary and sufficient conditions for their consequence relations. From this, we derive characterization results for S^fde; dS ^fde; crossS^fde. Second, the paper establishes complete sequent calculi for S^fde; dS^fde; crossS^fde. Among the other accomplishments of the paper, we generalize the semantics from Bochvar , Hallden , Deutsch  and Daniels , we provide a general recipe to define (a given family of) containment logics, we explore the single-premise/single-conclusion of S^fde; dS^fde; crossS^fde and the connections between crossS^fde and the logic Eq of equality by . Also, we present S^fde as a relevant logic of meaninglessness that follows the main philosophical tenets of Goddard and Routley . Finally, we discuss Routley's criticism to containment logic in light of our results, and overview some open issues.
Ciuni, R., Macaulay Ferguson, T., & Szmuc, D. (2018). Relevant Logics Obeying Component Homogeneity. THE AUSTRALASIAN JOURNAL OF LOGIC, 15(2), 301-361.
|Titolo:||Relevant Logics Obeying Component Homogeneity|
|Data di pubblicazione:||2018|
|Citazione:||Ciuni, R., Macaulay Ferguson, T., & Szmuc, D. (2018). Relevant Logics Obeying Component Homogeneity. THE AUSTRALASIAN JOURNAL OF LOGIC, 15(2), 301-361.|
|Appare nelle tipologie:||1.1 Articolo in rivista|