# Provably True Sentences Across Axiomatizations of Kripke’s Theory of Truth

@article{Nicolai2018ProvablyTS, title={Provably True Sentences Across Axiomatizations of Kripke’s Theory of Truth}, author={Carlo Nicolai}, journal={Studia Logica}, year={2018}, volume={106}, pages={101-130} }

We study the relationships between two clusters of axiomatizations of Kripke’s fixed-point models for languages containing a self-applicable truth predicate. The first cluster is represented by what we will call ‘$$\fancyscript{PKF}$$PKF-like’ theories, originating in recent work by Halbach and Horsten, whose axioms and rules (in Basic De Morgan Logic) are all valid in fixed-point models; the second by ‘$$\fancyscript{KF}$$KF-like’ theories first introduced by Solomon Feferman, that lose this…

## 12 Citations

THE MODAL LOGICS OF KRIPKE–FEFERMAN TRUTH

- PhilosophyThe Journal of Symbolic Logic
- 2020

A novel version of possible worlds semantics featuring both classical and nonclassical worlds is introduced and the completeness of a family of noncongruent modal logics whose internal logic is non classical with respect to this semantics is established.

KF, PKF, AND REINHARDT’S PROGRAM

- PhilosophyThe Review of Symbolic Logic
- 2022

In 'Some Remarks on Extending an Interpreting Theories with a Partial Truth Predicate' Reinhardt famously proposed an instrumentalist interpretation of the truth theory Kripke-Feferman (KF) in…

Nonclassical truth with classical strength. A proof-theoretic analysis of compositional truth over HYPE

- PhilosophyThe Review of Symbolic Logic
- 2020

By formulating the theory PKF over HYPE one obtains a theory that is sound with respect to fixed-point models, while being proof-theoretically on a par with its classical counterpart KF, thus matching the strength of predicative analysis.

On the Costs of Nonclassical Logic

- PhilosophyJ. Philos. Log.
- 2018

The reasons for this asymmetry are assessed by showing that the truth theoretic principles of PKF cannot be blamed: PKF with induction restricted to non-semantic vocabulary coincides in fact with what the restricted version of KF proves true.

On the Costs of Classical Logic

- PhilosophyErkenntnis
- 2021

This article compares classical (or -like) and nonclassical (or -like) axiomatisations of the fixed-point semantics developed by Kripke (J Philos 72(19): 690–716, 1975). Following the line of…

Comparing Axiomatic Theories of Truth

- Philosophy
- 2019

S U M M A R Y : This paper is a direct continuation of (Łełyk, Wcisło, 2017), where one particular way of comparing axiomatic theories of truth was discussed at length in the context of extensions of…

Systems for non-reflexive consequence

- Philosophy
- 2020

. Substructural logics and their application to logical and semantic paradoxes have been extensively studied. In the paper, we study theories of naïve consequence and truth based on a non-reflexive…

Iterated reflection over full disquotational truth

- PhilosophyJ. Log. Comput.
- 2017

This article shows how in the context of a weaker logic, which is called Basic De Morgan Logic, a collection of Tarski-biconditionals can coherently start with such a fully disquotational truth theory and arrive at a strong compositional truth theory by applying a natural uniform reflection principle a finite number of times.

Is the HYPE about strength warranted?

- PhilosophySynthese
- 2022

In comparing classical and non-classical solutions to the semantic paradoxes arguments relying on strength have been influential. In this paper I argue that non-classical solutions should preserve…

THE POWER OF NAIVE TRUTH

- PhilosophyThe Review of Symbolic Logic
- 2020

Abstract Nonclassical theories of truth that take truth to be transparent have some obvious advantages over any classical theory of truth (which must take it as nontransparent on pain of…

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