ICLA 2017: Logic and Its Applications pp 27-47

# Semantics and Proof Theory of the Epsilon Calculus

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10119)

## Abstract

The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. The application of this undervalued formalism has been hampered by the absence of well-behaved proof systems on the one hand, and accessible presentations of its theory on the other. One significant early result for the original axiomatic proof system for the $$\varepsilon$$-calculus is the first epsilon theorem, for which a proof is sketched. The system itself is discussed, also relative to possible semantic interpretations. The problems facing the development of proof-theoretically well-behaved systems are outlined.

## Keywords

Choice Function Intuitionistic Logic Proof Theory Sequent Calculus Proof Tree
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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