The undecidability of proof search when equality is a logical connective

One proof-theoretic approach to equality in quantificational logic treats equality as a logical connective: in particular, term equality can be given both left and right introduction rules in a sequent calculus proof system. We present a particular example of this approach to equality in a first-ord...

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Published inAnnals of mathematics and artificial intelligence Vol. 90; no. 5; pp. 523 - 535
Main Authors Miller, Dale, Viel, Alexandre
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.05.2022
Springer
Springer Nature B.V
Springer Verlag
Subjects
Artificial Intelligence
Calculus
Complex Systems
Computer Science
Logic
Logic in Computer Science
Mathematics
Variables
Undecidability
03F03
Equality
Unification
Sequent calculus
sequent calculus
unification
equality
undecidability
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ISSN1012-2443
1573-7470
DOI10.1007/s10472-021-09764-0

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Summary:One proof-theoretic approach to equality in quantificational logic treats equality as a logical connective: in particular, term equality can be given both left and right introduction rules in a sequent calculus proof system. We present a particular example of this approach to equality in a first-order logic setting in which there are no predicate symbols (apart from equality). After we illustrate some interesting applications of this logic, we show that provability in this logic is undecidable.
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ISSN:1012-2443
1573-7470
DOI:10.1007/s10472-021-09764-0