A cut rule in proof theory introduces an intermediate conclusion within a deductive proof. This intermediate step is then utilized…
Constructive mathematics emphasizes mathematical objects that are provably constructible and computable. It avoids non-constructive proofs, like those relying on the…
Constructive logic emphasizes explicit proofs of existence, demanding a concrete construction rather than indirect reasoning. It's a foundational approach in…
A conservative extension adds new axioms or rules to a theory without altering the truth of existing statements. This ensures…
Categorical logic, rooted in category theory, explores object categorization and the logical underpinnings of categories. It provides a formal framework…
The bottom symbol (⊥), also known as the symbol for contradiction or absurdity, is a fundamental concept in logic. It…
The Brouwer-Heyting-Kolmogorov (BHK) interpretation equates statement truth with proof existence, forming the core of constructivist logic. It emphasizes constructive evidence…
A provability predicate is a mathematical function that determines whether a statement is provable within a given formal system. It's…
Affine logics, a specialized branch of linear logic, explore the properties of affine transformations and their direct impact on logical…
Abelian logic is a specific type of relevance logic. It notably rejects the inference rule of contraction while accepting the…