Book contents
- Frontmatter
- Contents
- Preface
- Part I Foundations
- Part II Typed truth
- Part III Type-free truth
- 10 Typed and type-free theories of truth
- 11 Reasons against typing
- 12 Axioms and rules
- 13 Axioms for type-free truth
- 14 Classical symmetric truth
- 15 Kripke–Feferman
- 16 Axiomatizing Kripke's theory in partial logic
- 17 Grounded truth
- 18 Alternative evaluation schemata
- 19 Disquotation
- Part IV Ways to the truth
- Index of systems
- Bibliography
- Index
18 - Alternative evaluation schemata
from Part III - Type-free truth
Published online by Cambridge University Press: 05 February 2015
- Frontmatter
- Contents
- Preface
- Part I Foundations
- Part II Typed truth
- Part III Type-free truth
- 10 Typed and type-free theories of truth
- 11 Reasons against typing
- 12 Axioms and rules
- 13 Axioms for type-free truth
- 14 Classical symmetric truth
- 15 Kripke–Feferman
- 16 Axiomatizing Kripke's theory in partial logic
- 17 Grounded truth
- 18 Alternative evaluation schemata
- 19 Disquotation
- Part IV Ways to the truth
- Index of systems
- Bibliography
- Index
Summary
The Kripke–Feferman theory is based on Strong Kleene logic as an evaluation schema. Kripke (1975) formulated his semantic construction is such a way that other evaluation schemata can be used as well. In the definition of Λ on p. 194 the relation ⊨SK of being valid in a model under Strong Kleene logic can be replaced with other notions of validity in a model. The relation replacing ⊨SK must satisfy a certain condition; otherwise the operation corresponding to Ë may lack fixed points. Here I will not go into general results on admissible evaluation schemata; rather I shall focus on axiomatic theories akin to KF but based on two alternative evaluation schemata.
First, I consider the standard Weak Kleene logic with only truth-value gaps and no gluts. In Strong Kleene logic a disjunction of two sentences is true if at least one disjunct is true, even when the other disjunct lacks a truth value. In Weak Kleene logic a sentence is evaluated as neither true nor false if one of its components lacks a truth value. The truth tables for Weak Kleene logic are thus easily described: whenever there is a truth-value gap among the entries of a line the value of the complex sentence will also be a gap. All other lines coincide with the lines of the truth tables of classical logic. One can easily develop Kripke's semantic construction for Weak Kleene logic.
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- Information
- Axiomatic Theories of Truth , pp. 249 - 252Publisher: Cambridge University PressPrint publication year: 2014