Next Article in Journal
A Study Concerning Soft Computing Approaches for Stock Price Forecasting
Next Article in Special Issue
Hybrid Deduction–Refutation Systems
Previous Article in Journal
Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable—Part II: Extremal Points, Convexity, Periodicity
Previous Article in Special Issue
Deontic Logics as Axiomatic Extensions of First-Order Predicate Logic: An Approach Inspired by Wolniewicz’s Formal Ontology of Situations
Open AccessArticle

Deduction in Non-Fregean Propositional Logic SCI

Institute of Philosophy, University of Warsaw, 00–927 Warsaw, Poland
*
Author to whom correspondence should be addressed.
Axioms 2019, 8(4), 115; https://doi.org/10.3390/axioms8040115
Received: 5 September 2019 / Revised: 11 October 2019 / Accepted: 14 October 2019 / Published: 17 October 2019
(This article belongs to the Special Issue Deductive Systems)
We study deduction systems for the weakest, extensional and two-valued non-Fregean propositional logic SCI . The language of SCI is obtained by expanding the language of classical propositional logic with a new binary connective ≡ that expresses the identity of two statements; that is, it connects two statements and forms a new one, which is true whenever the semantic correlates of the arguments are the same. On the formal side, SCI is an extension of classical propositional logic with axioms characterizing the identity connective, postulating that identity must be an equivalence and obey an extensionality principle. First, we present and discuss two types of systems for SCI known from the literature, namely sequent calculus and a dual tableau-like system. Then, we present a new dual tableau system for SCI and prove its soundness and completeness. Finally, we discuss and compare the systems presented in the paper. View Full-Text
Keywords: non-Fregean logic; identity connective; sentential calculus with identity; situational semantics; deduction; (dual) tableau; Gentzen system non-Fregean logic; identity connective; sentential calculus with identity; situational semantics; deduction; (dual) tableau; Gentzen system
Show Figures

Figure 1

MDPI and ACS Style

Golińska-Pilarek, J.; Welle, M. Deduction in Non-Fregean Propositional Logic SCI. Axioms 2019, 8, 115.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop