Number of Extensions of Non-Fregean Logics
نویسندگان
چکیده
We show that there are continuum many different extensions of SCI (the basic theory of non-Fregean propositional logic) that lie below WF (the Fregean extension) and are closed under substitution. Moreover, continuum many of them are independent from WB (the Boolean extension), continuum many lie above WB and are independent from WH (the Boolean extension with only two values for the equality relation), and only countably many lie between WH and WF.
منابع مشابه
On some many-valued abstract logics and their Epsilon-T-style extensions
Logical systems with classical negation and means for sentential or propositional self-reference involve, in some way, paradoxical statements such as the liar. However, the paradox disappears if one replaces classical by an appropriate non-classical negation such as a paraconsistent one (no paradox arises if the liar is both true and false). We consider a non-Fregean logic which is a revised an...
متن کاملFregean logics
According to Frege’s principle the denotation of a sentence coincides with its truthvalue. The principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense. A 2nd-order matrix is an algebra together with an algebraic closed set system on its universe. A ded...
متن کاملRasiowa-Sikorski proof system for the non-Fregean sentential logic SCI
The sentential logic SCI is obtained from the classical sentential calculus by adding a new identity connective ≡ (different from ↔) and axioms which say ”α ≡ β” means ”α is identical to β” . From the axioms for ≡ it follows that the range of sentences has at least two elements. No other special presupposition about the meaning of ’is identical to’ nor the range of sentences are assumed. Any ad...
متن کاملDenotational Semantics for Modal Systems S3-S5 Extended by Axioms for Propositional Quantifiers and Identity
There are logics where necessity is defined by means of a given identity connective: φ := φ ≡ ⊤ (⊤ is a tautology). On the other hand, in many standard modal logics the concept of propositional identity (PI) φ ≡ ψ can be defined by strict equivalence (SE) (φ ↔ ψ). All these approaches to modality involve a principle that we call the Collapse Axiom (CA): “There is only one necessary proposition....
متن کاملEQ-logics with delta connective
In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binary...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Philosophical Logic
دوره 34 شماره
صفحات -
تاریخ انتشار 2005