Quantitative deduction and its fixpoint theory

Quantitative Deduction and its Fixpoint Theory

On the Fixpoint Theory of Equality and Its Applications

In the current paper we first show that the fixpoint theory of equality is decidable. The motivation behind considering this theory is that second-order quantifier elimination techniques based on a theorem given in [16], when successful, often result in such formulas. This opens many applications, including automated theorem proving, static verification of integrity constraints in databases as ...

On Natural Deduction in First-Ortder Fixpoint Logics

In the current paper we present a powerful technique of obtaining natural deduction proof systems for rst-order xpoint logics. The term xpoint logics refers collectively to a class of logics consisting of modal logics with modalities deenable at meta-level by xpoint equations on formulas. The class was found very interesting as it contains most logics of programs with e.g. dynamic logic, tempor...

Deduction modulo theory

Contemporary proof theory goes into several directions at the same time. One of them aims at analysing proofs, propositions, connectives, etc., that is at decomposing these objects into more atomic ones. This often leads to design systems that are weaker than Predicate logic, but that have better algebraic or computational properties, and to try to reconstruct part of Predicate logic on top of ...

Alternating Fixpoint Theory for Logic Programswith