Second-Order Classical Sequent Calculus

LKQ and LKT: Sequent calculi for second order logic based upon dual linear decompositions of classical implication by

The Isomorphism Between Expansion Proofs and Multi-Focused Sequent Proofs

The sequent calculus is often criticized for requiring proofs to contain large amounts of low-level syntactic details that can obscure the essence of a given proof. Because each inference rule introduces only a single connective, sequent proofs can separate closely related steps—such as instantiating a block of quantifiers—by irrelevant noise. Moreover, the sequential nature of sequent proofs f...

A multi-focused proof system isomorphic to expansion proofs

The sequent calculus is often criticized for requiring proofs to contain large amounts of low-level syntactic details that can obscure the essence of a given proof. Because each inference rule introduces only a single connective, sequent proofs can separate closely related steps—such as instantiating a block of quantifiers—by irrelevant noise. Moreover, the sequential nature of sequent proofs f...

On the Construction of Analytic Sequent Calculi for Sub-classical Logics

Proof theory reveals a wide mosaic of possibilities for sub-classical logics. These are logics that are strictly contained (as consequence relations) in classical logic. Thus, by choosing a subset of axioms and derivation rules that are derivable in (some proof system for) classical logic, one easily obtains a (proof system for a) sub-classical logic. Various important and useful non-classical ...

Proof Search in the Intuitionistic Sequent Calculus

The use of Herbrand functions (sometimes called Skolemization) plays an important role in classical theorem proving and logic programming. We define a notion of Herbrand functions for the full intuitionistic predicate calculus. This definition is based on the view that the proof-theoretic role of Herbrand functions (to replace universal quantifiers), and of unification (to find instances corres...