A three-valued doxastic logic based on Kleene’s and Bochvar’s ideas
A three-valued doxastic logic based on Kleene’s and Bochvar’s ideas
Author(s): Janusz WesserlingSubject(s): Logic, Syntax, Semantics, Philosophy of Language
Published by: Wydawnictwo Naukowe Uniwersytetu Kardynała Stefana Wyszyńskiego w Warszawie
Keywords: doxastic logic; strong belief; Kleene’s strong three-valued logic; internal connectives; external connectives; completeness theorem;
Summary/Abstract: In this paper, I shall propose the construction of a three-valued logic of beliefs, which I call: LSB3_1 (short for: Three-valued Logic for a type of Strong Belief). I shall also state and prove the completeness of LSB3_1 with respect to a given semantics. LSB3_1 is based on preformal assumptions and intuitions, which are stated in section 1. Section 2 includes the syntax and division of LSB3_1 statements into internal and external. Section 3 presents the semantics of LSB3_1, as well as a number of tautologies and non-tautological formulae in LSB3_1 with their intuitive interpretation. The axiomatic system for LSB3_1 and its comparison to Kleene’s strong logic are provided in section 4. The completeness theorem for LSB3_1 is presented in section 5. I shall define the term conjunctive normal form and provide lemmas which lead to proving the reduction of the LSB3_1 language formulae before proving the completeness theorem.
Journal: Studia Philosophiae Christianae
- Issue Year: 55/2019
- Issue No: 4
- Page Range: 89-113
- Page Count: 25
- Language: English