A Simplified and Improved Free-Variable Framework for Hilbert's epsilon as an Operator of Indefinite Committed Choice

04/13/2011
by   Claus-Peter Wirth, et al.
0

Free variables occur frequently in mathematics and computer science with ad hoc and altering semantics. We present the most recent version of our free-variable framework for two-valued logics with properly improved functionality, but only two kinds of free variables left (instead of three): implicitly universally and implicitly existentially quantified ones, now simply called "free atoms" and "free variables", respectively. The quantificational expressiveness and the problem-solving facilities of our framework exceed standard first-order and even higher-order modal logics, and directly support Fermat's descente infinie. With the improved version of our framework, we can now model also Henkin quantification, neither using quantifiers (binders) nor raising (Skolemization). We propose a new semantics for Hilbert's epsilon as a choice operator with the following features: We avoid overspecification (such as right-uniqueness), but admit indefinite choice, committed choice, and classical logics. Moreover, our semantics for the epsilon supports reductive proof search optimally.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

07/28/2012

FMLtoHOL (version 1.0): Automating First-order Modal Logics with LEO-II and Friends

A converter from first-order modal logics to classical higher- order log...
07/26/2019

Extensional Higher-Order Paramodulation in Leo-III

Leo-III is an automated theorem prover for extensional type theory with ...
05/19/2019

Is Free Choice Permission Admissible in Classical Deontic Logic?

In this paper, we explore how, and if, free choice permission (FCP) can ...
07/15/2021

Tableaux for Free Logics with Descriptions

The paper provides a tableau approach to definite descriptions. We focus...
10/11/2019

Internal Calculi for Separation Logics

We present a general approach to axiomatise separation logics with heapl...
06/18/2014

Typed Hilbert Epsilon Operators and the Semantics of Determiner Phrases (Invited Lecture)

The semantics of determiner phrases, be they definite de- scriptions, in...
07/11/2018

Everybody's Got To Be Somewhere

The key to any nameless representation of syntax is how it indicates the...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.