A semantical study of some propositional calculi

This paper provides a semantical analysis of da Costa’s propositional calculi C𝑛 and, in particular, of the limit case C𝜔, which had previously lacked a valuationbased semantics. Loparić constructs a positive answer to the question of whether C𝜔 can be semantically characterized similarly to the calculi C𝑛 for 1 ⩽ 𝑛 < 𝜔. The work introduces formal definitions of semi-valuations and valuations, establishes soundness and completeness theorems, and develops procedures for the construction of semantic decision tables. These results deepen our understanding of paraconsistent logics and open the way for similar semantic treatments in other non-classical systems containing intuitionistic implicative logic.