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Automated theorem proving is the proving of mathematical theorems by a computer program.
9
votes
Accepted
First order satisfiability that doesn't have finite models
Here's an amusing approach by Brock-Nannestad and Schürmann:
Truthful Monadic Abstractions
The idea is to try to translate first-order sentences into monadic first-order logic, by "forgetting" some …
2
votes
Automated proving that a program doesn't halt
In contradiction with Gurkenglas' answer, there actually is a community of scientists who work on proving non-termination of programs in various language and formalisms.
An obvious approach would be …
14
votes
Accepted
Logical Reations for an Impredicative System in a Predicative MetaTheory
In general, what we usually call the logical relations argument isn't really linked to impredicativity: the main idea is simply to interpret terms in some abstract algebra $\cal A$, and to represent t …
8
votes
What paradigm of automated theorem proving is appropriate for Principia Mathematica-style fo...
Several points:
As far as I know, Principia Mathematica uses essentially a formalization of set theory using a typed first order logic. It would therefore be tempting to use a first-order automated …
1
vote
Accepted
Formalized priority argument
Computability theory in general has been somewhat under-formalized. The short answer is that most theorems of computability theory do not pass one of the three tests for formalization:
A proof that …
3
votes
Accepted
State of the Art for the Monadic Class?
I found signs that such a decision procedure was implemented in the (general purpose) theorem prover SPASS.
In particular see the thesis of Ann-Christin Knoll, On Resolution
Decision Procedures
for …