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Fundamental Propositional Logic with Preconditional: Strong Completeness, Finite Model Property, and Modal Translations
Zhicheng Chen
Fundamental logic (Holliday 2023) is a non-classical logic based only on the introduction and elimination rules for conjunction, disjunction, and negation in a Fitch-style natural…
An Intermediate Logic Contained in Medvedev's Logic with Disjunction Property
Zhicheng Chen
Let be the superintuitionistic logic defined by the axiom $\boldsymbol{su} = ((\neg p\to q)\land(\neg q\to p) \rightarrow r \vee s) \to ( p \rightarrow r) \vee(q \rig…
Fundamental Propositional Logic with Strict Implication
Zhicheng Chen
Fundamental logic was introduced by Wesley Holliday (2023) to unify intuitionistic logic and quantum logic from a proof-theoretic perspective, capturing the logic determined solely…
The Logics of Individual Medvedev Frames
Zhicheng Chen, Yifeng Ding
Let -Medvedev's logic be the intuitionistic logic of Medvedev frames based on the non-empty subsets of a set of size , which we call -Medvedev frames. Whil…
A unified relational semantics for BPL, IPL and OL -- axiomatization without disjunction
Zhicheng Chen
In this paper, we propose a relational semantics of propositional language, which unifies the relational semantics of intuitionistic logic, Visser's Basic Propositional Logic and o…