Questions tagged [automated-theorem-proving]

Automated theorem proving is the proving of mathematical theorems by a computer program.

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Is there a known automatic proof of the independence of the continuum hypothesis?

In 2002, L.C. Paulson gave a mechanized proof of the consistency of the axiom of choice by formalizing $V=L$ and its consistency. We could ask whether there is a formalized proof of the independence ...
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On the interpretation of coinduction in type theory

The notion of (co)datatype can be modeled satisfactorily in category theory as fixed-points of polynomial functors. Then, (co)induction principles are derived from initial algebras/terminal ...
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extracting/ exploiting similarity of SAT instances by solver

suppose that two SAT formulas on different variables $F_1, F_2$ are given on the input that are known to be true and the problem is to build an algorithm that finds a solution to each. the formulas ...
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What logic do refinement types correspond to?

I'm interested in applicability of refinement types to theorem-proving hence the questions about their logical expressiveness. Let's say, we have a type system which corresponds to some logic ...
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95 views

A reasonable proof strategy for formally verifying Ukkonen's algorithm?

What's a reasonable proof strategy to formally verify Ukkonen's algorithm in, say, Coq? The ingredients as far as I can tell would be: some form of separation logic to be able to reason about the ...
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53 views

Formalization of Interval Newton methods in a proof assistant or theorem prover

I am undertaking the task of formalizing Interval Newton Methods in Isabelle. To the best of my knowledge this hasn't been formalized in other proof assistants or theorem provers. However, I want to ...
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496 views

Is it possible to derive induction by extending CoC with recursion?

Suppose we extended the CoC with primitive recursion; that is, we added a term µ x . t such that equality allowed unrolling recursive terms: ...
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285 views

Are there applications of experimental mathematics in TCS?

In recent years there have been major, diverse, sometimes surprising advances in experimental mathematics [1] for a variety of sophisticated uses such as developing/deriving exact formulas, theorem ...
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381 views

Theorem prover fails to find simple set theory proof?

I am trying to use an automated theorem prover (SNARK) to prove a theorem in first-order logic. Tarski claims in his "a work on mereology" that the goal is provable from assertions 1-3 but he does ...
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76 views

Regaining decidability by adding axioms that model real world situation

It is known that first order logic is too general to be decidable. Adding axioms with special meaning (e.g. expressing notions such as necessity/obligation, provability, etc.) leads us to modal logics ...
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Journals or conferences to submit formally verified libraries?

This is a soft question aimed at understanding whether there is any value to publishing formally verified libraries. I have formally verified (in Coq) implementations of: synthetic differential ...
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136 views

Do problems have to be statable in $\Pi_1$ to use Levin's universal search to find short proofs if P=NP

In If P=NP, could we obtain proofs of Goldbach's Conjecture etc.? it talks about the hypothetical world where P=NP and using the proof of it to prove a problem/theorem assuming that it has a short ...