
Trakhtenbrot's Theorem in Coq: Finite Model Theory through the Constructive Lens
We study finite firstorder satisfiability (FSAT) in the constructive se...
read it

Amalgamation is PSPACEhard
The finite models of a universal sentence Φ in a finite relational signa...
read it

Splitting Proofs for Interpolation
We study interpolant extraction from local firstorder refutations. We p...
read it

On the construction of explosive relation algebras
Fork algebras are an extension of relation algebras obtained by extendin...
read it

Employing fuzzy intervals and loopbased methodology for designing structural signature: an application to symbol recognition
Motivation of our work is to present a new methodology for symbol recogn...
read it

Constructing Initial Algebras Using Inflationary Iteration
An old theorem of Adámek constructs initial algebras for sufficiently co...
read it

Hilbert's Tenth Problem in Coq
We formalise the undecidability of solvability of Diophantine equations,...
read it
Trakhtenbrot's Theorem in Coq, A Constructive Approach to Finite Model Theory
We study finite firstorder satisfiability (FSAT) in the constructive setting of dependent type theory. Employing synthetic accounts of enumerability and decidability, we give a full classification of FSAT depending on the firstorder signature of nonlogical symbols. On the one hand, our development focuses on Trakhtenbrot's theorem, stating that FSAT is undecidable as soon as the signature contains an at least binary relation symbol. Our proof proceeds by a manyone reduction chain starting from the Post correspondence problem. On the other hand, we establish the decidability of FSAT for monadic firstorder logic, i.e. where the signature only contains at most unary function and relation symbols, as well as the enumerability of FSAT for arbitrary enumerable signatures. All our results are mechanised in the framework of a growing Coq library of synthetic undecidability proofs.
READ FULL TEXT
Comments
There are no comments yet.