Kleene connectives extend classical logic with a third truth value (undefined/unknown). They are crucial for handling indeterminate propositions and are…
Inconsistent arithmetic refers to a mathematical system where contradictions can be proven, violating the fundamental principle of consistency. This makes…
A hierarchy ranks entities based on criteria, seen in organizational structures and set theory. Tarski's and cumulative hierarchies are key…
A formal system is a set of symbols and rules for manipulating them, used to derive statements or theorems in…
A first-order theory formalizes mathematical reasoning using first-order logic. It defines relationships between individuals, properties, and relations, forming the foundation…
FDE is a logical system that allows propositions to be both true and false, or neither, rejecting the law of…
A finitary formal system uses only finite operations, proofs, and expressions. It relies on objects constructible in a finite number…
Extensional logic focuses on the actual sets of things terms refer to, rather than their meanings. Truth depends only on…
A specialized field of modal logic focusing on formalizing reasoning about knowledge and belief. It uses modal operators to represent…
An effectively decidable theory is a formal system where an algorithm can definitively prove any statement as either true or…