Set Constraints in Some Equational Theories

An Equational Re-engineering of Set Theories

New successes in dealing with set theories by means of stateof-the-art theorem-provers may ensue from terse and concise axiomatizations, such as can be moulded in the framework of the (fully equational) Tarski-Givant map calculus. In this paper we carry out this task in detail, setting the ground for a number of experiments.

Tree Automata with Equality Constraints Modulo Equational Theories

This paper presents new classes of tree automata combining automata with equality test and automata modulo equational theories. We believe that this class has a good potential for application in e.g. software verification. These tree automata are obtained by extending the standard Horn clause representations with equational conditions and rewrite systems. We show in particular that a generalize...

Equational Theories in CERES

Cut-elimination is the most important proof transformation in logic. Equality is a central paradigm in mathematics and plays a key role in automated deduction. Therefore its importance awakes the necessity of integrating equality into existing cut-elimination methods. In this paper we extend the resolution-based method of cut-elimination CERES to CERES-e by adding equality (and paramodulation t...

Equational Logic and Equational Theories of Algebras

Some Set Theories Are More Equal

The proof of independence of the Continuum Hypothesis by Paul Cohen in 1963 and the avalanche of additional independence results was the trigger to a very intensive discourse about the future of Set Theory and its foundational role in Mathematics. It will be only fair to say that while the invention of forcing initiated the blooming of Set Theory as a technical mathematical discipline, it had a...