(Star-based) four-valued Kripke-style semantics for some neighbors of E, R, T

This paper investigates four-valued Kripke-style semantics (with star (*) operation) for three sorts of logics, which can be regarded as paraconsistent, Ockham, and Boolean neighbors of the most famous relevance systems E of Entailment, R of Relevance, and T of Ticket Entailment. We first introduce some paraconsistent cousins of E and R, provide Kripke-style semantics for them, and prove soundness and completeness. We then further consider Kripke-style semantics with star (*) operation, briefly *-Kripke-style semantics, for them. We next introduce some Ockham neighbors of E and R. After providing Kripke-style semantics for them, we prove soundness and completeness. We finally introduce several Boolean neighbors of E, R, and T. We provide *-Kripke-style semantics for not merely the Boolean neighbors but also the Ockham neighbors, and prove soundness and completeness.