On the logic of factual equivalence (Q2804475)

The paper considers the notion of a factual equivalence understood as a form of ``sameness of content'', which is different from synonymy. The former is given a broader meaning than the latter, e.g., ``Hesperus is Phosphorus'' and ``Hesperus is Hesperus'' are factually equivalent but not synonymous. NEWLINENEWLINEThe author constructs a logical system in the language with conjunction, disjunction and negation, which is designed to determine the set of sentences factually equivalent by virtue of their logical form only. The system consists of the following axiom schemata and rules of inference: NEWLINENEWLINEA1.~\(A \approx \neg\neg A\); NEWLINENEWLINEA2.~\(A \approx A \wedge A\); NEWLINENEWLINEA3.~\(A \wedge B \approx B \wedge A\); NEWLINENEWLINEA4.~\(A \wedge (B \wedge C) \approx (A \wedge B) \wedge C\); NEWLINENEWLINEA5.~\(A \approx A \vee A\); NEWLINENEWLINEA6.~\(A \vee B \approx B \vee A\); NEWLINENEWLINEA7.~\(A \vee (B \vee C) \approx (A \vee B) \vee C\); NEWLINENEWLINEA8.~\(\neg(A \wedge B) \approx \neg A \vee \neg B\); NEWLINENEWLINEA9. \(\neg(A \vee B) \approx \neg A \wedge \neg B\); NEWLINENEWLINEA10. \(A \wedge (B \vee C) \approx (A \wedge B) \vee (A \wedge C)\). NEWLINENEWLINER1.~\(A \approx B / B \approx A\); NEWLINENEWLINER2.~\(A \approx B, B \approx C / A \approx C\); NEWLINENEWLINER3.~\(A \approx B / A \wedge C \approx B \wedge C\); NEWLINENEWLINER4.~\(A \approx B / A \vee C \approx B \vee C\). NEWLINENEWLINE(Adding to this system the axiom dual to A10, namely NEWLINENEWLINEA11.~\(A \vee (B \wedge C) \approx (A \vee B) \wedge (A \vee C)\),NEWLINENEWLINE which is not provable in the formulated system, results in Angell's first-degree system for analytic equivalence.) The system is provided with two semantics, ``both formulated in terms of the notion of a situation's being fittingly described by a linguistic item'', and is shown to be sound and complete with respect to the semantics so formulated.