Strict Conditionals
The Paradoxes of Strict Implication
The Explosion of Contradictions
Lewis’ Argument for Explosion
Conditional Logics
Introduction
Some More Problematic Inferences
Intuitionistic Logic
Introduction
Intuitionism: The Rationale
Possible Worlds Semantics for Intuitionism
6.4
Tableaux for Intuitionistic Logic
Many-valued Logics
Introduction
Many-valued Logic: The General Structure
The 3-valued Logics of Kleene and Łukasiewicz
LP and RM3
Many-valued Logics and Conditionals
7.6 Truth-value Gluts: Inconsistent Laws
Truth-value Gluts: Paradoxes of Self-reference
Truth-value Gaps: Denotation Failure
Truth-value Gaps: Future Contingents
Supervaluations, Modality and Many-valued Logic
First Degree Entailment
Introduction
The Semantics of FDE
Tableaux for FDE
FDE and Many-valued Logics
The Routley Star
Paraconsistency and the Disjunctive Syllogism
Logics with Gaps, Gluts and Worlds
Introduction
Adding →
Tableaux for K4
Non-normal Worlds Again
Tableaux for N4
Star Again
Impossible Worlds and Relevant Logic
Logics of Constructible Negation
Relevant Logics
Introduction
The Logic B
The Ternary Relation
Fuzzy Logics
Introduction
Sorites Paradoxes
. . . and Responses to Them
The Continuum-valued Logic Ł
Appendix: Many-valued Modal Logics
Introduction
General Structure
Modal FDE
Future Contingents Revisited
Quantification and Identity
Classical First-order Logic
Introduction
Syntax
Semantics
Tableaux
Identity
Some Philosophical Issues
Free Logics
Introduction
Syntax and Semantics
Tableaux
Free Logics: Positive, Negative and Neutral
Quantification and Existence
Identity in Free Logic
Constant Domain Modal Logics
Introduction
Constant Domain
K Variable Domain Modal Logics
Introduction
Prolegomenon
Variable Domain K and its Normal Extensions
Necessary Identity in Modal Logic
Introduction
Necessary Identity
The Negativity Constraint
Rigid and Non-rigid Designators
Names and Descriptions
Many-valued Logics
Introduction
Quantified Many-valued Logics
∀ and ∃
Some 3-valued Logics
Their Free Versions
Existence and Quantification
Neutral Free Logics
Identity
Non-classical Identity
Priest, Graham. 2008 [2001]. An Introduction to Non-Classical Logic: From If to Is, 2nd edn. Cambridge: Cambridge University.
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