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**1 - 5**of**5**### Completeness Proof of Functional Logic, A Formalism with Variable-Binding Nonlogical Symbols

, 1995

"... We know extensions of first order logic by quantifiers of the kind “there are uncountable many...”, “most... ” with new axioms and appropriate semantics. Related are operations such as “set of x, such that...”, Hilbert’s ε-operator, Churche’s λ-notation, minimization and similar ones, which also bin ..."

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We know extensions of first order logic by quantifiers of the kind “there are uncountable many...”, “most... ” with new axioms and appropriate semantics. Related are operations such as “set of x, such that...”, Hilbert’s ε-operator, Churche’s λ-notation, minimization and similar ones, which also bind a variable within some expression, the meaning of which is however partly defined by a translation into the language of first order logic. In this paper a generalization is presented that comprises arbitrary variable-binding symbols as non-logical operations. The axiomatic extension is determined by new equality-axioms; models allocate functionals to variable-binding symbols. The completeness of this system of the so called functional logic of 1st order will be proved. Mathematics Subject Classification: 03C80, 03B99. 1

### Epsilon, Delta, and Speed-Ups WORK in PROGRESS

"... Abstract. This paper studies the applicability of Hilbert’s ε-calculus in automated reasoning, in particular its incorporation in free-variable tableaux is investigated. Based on this study a careful comparison between δε-tableaux [1] and δ-tableaux [8] becomes possible. Finally, in the spirit of [8 ..."

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Abstract. This paper studies the applicability of Hilbert’s ε-calculus in automated reasoning, in particular its incorporation in free-variable tableaux is investigated. Based on this study a careful comparison between δε-tableaux [1] and δ-tableaux [8] becomes possible. Finally, in the spirit of [8], a new liberalization of the δ-rule [3] is defined. This liberalization allows a non-elementary speed-up over δ-tableaux. 1

### (Current Issues in Linguistic Theory 114) THE EPSILON OPERATOR AND E-TYPE PRONOUNS

"... In this paper we attempt to provide a homogeneous description of definite and indefinite noun phrases. We therefore assume one semantic representation for one interpretation that the definite article the and the indefinite article a share. Our starting point is the classical theory of ..."

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In this paper we attempt to provide a homogeneous description of definite and indefinite noun phrases. We therefore assume one semantic representation for one interpretation that the definite article the and the indefinite article a share. Our starting point is the classical theory of