Related papers: Supervaluations, truth, and intuitionistic logic
In this paper we show how to introduce a conditional to Kripke's theory of truth that respects the deduction theorem for the consequence relation associated with the theory. To this effect we develop a novel supervaluational framework,…
The paper explores applications of Kripke's theory of truth to semantics for anti-luck epistemology, that is, to subjunctive theories of knowledge. Subjunctive theories put forward modal or subjunctive conditions to rule out knowledge by…
We compare the conceptual strength of two axiomatic theories of truth: KF and WKF. The first one has been designed to capture Kripke's fixed-point construction based on Strong Kleene logic. The second one is based on the Weak Kleene…
Supervaluational fixed-point theories of formal truth aim to amend an important shortcoming of fixed-point theories based on the Strong Kleene logic, namely, accounting for the truth of classical validities. In a celebrated paper, Andrea…
Supervaluational fixed-point semantics for truth cannot be axiomatized because of its recursion-theoretic complexity. Johannes Stern (\emph{Supervaluation-Style Truth Without Supervaluations}, Journal of Philosophical Logic, 2018) proposed…
On the basis of elementary thinking about language functioning, a solution of truth paradoxes is given and a corresponding semantics of a truth predicate is founded. It is shown that it is precisely the two-valued description of the maximal…
We study fixpoints of operators on lattices. To this end we introduce the notion of an approximation of an operator. We order approximations by means of a precision ordering. We show that each lattice operator O has a unique most precise or…
It is known that intuitionistic Kripke semantics can be generalized so that it can treat arbitrary propositional connectives characterized by truth functions. We extend this generalized Kripke semantics to first-order logic, and study how…
Bernays introduced a method for proving underivability results in propositional calculi by truth tables. In general, this motivates an investigations of how to find, given a propositional logic, a finite-valued logic which has as few…
We develop a fixed-point extension of quantitative equational logic and give semantics in one-bounded complete quantitative algebras. Unlike previous related work about fixed-points in metric spaces, we are working with the notion of…
In recent years, the logic of questions and dependencies has been investigated in the closely related frameworks of inquisitive logic and dependence logic. These investigations have assumed classical logic as the background logic of…
We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…
This paper presents a novel possible worlds semantics, designed to elucidate the underpinnings of ultrafinitism. By constructing a careful modification of the well-known Kripke models for inuitionistic logic, we seek to extend our…
Intuitionistic Propositional Logic is proved to be an infinitely many valued logic by Kurt G\"odel (1932), and it is proved by Stanis{\l}aw Ja\'skowski (1936) to be a countably many valued logic. In this paper, we provide alternative proofs…
In this paper we show that the intuitionistic fixed point theory FiX^{i}(X) over set theories T is a conservative extension of T if T can manipulate finite sequences and has the full foundation schema.
Questions concerning the proof-theoretic strength of classical versus non-classical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of…
I show that the logic $\textsf{TJK}^{d+}$, one of the strongest logics currently known to support the naive theory of truth, is obtained from the Kripke semantics for constant domain intuitionistic logic by (i) dropping the requirement that…
In this paper we consider the class of truth-functional many-valued logics with a finite set of truth-values. The main result of this paper is the development of a new \emph{binary} sequent calculi (each sequent is a pair of formulae) for…
Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…