
Trakhtenbrot's Theorem in Coq, A Constructive Approach to Finite Model Theory
We study finite firstorder satisfiability (FSAT) in the constructive se...
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The Complexity of Prenex Separation Logic with One Selector
We first show that infinite satisfiability can be reduced to finite sati...
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Church's thesis and related axioms in Coq's type theory
"Church's thesis" (𝖢𝖳) as an axiom in constructive logic states that eve...
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Amalgamation is PSPACEhard
The finite models of a universal sentence Φ in a finite relational signa...
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Constructing Initial Algebras Using Inflationary Iteration
An old theorem of Adámek constructs initial algebras for sufficiently co...
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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...
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Separating Data Examples by Description Logic Concepts with Restricted Signatures
We study the separation of positive and negative data examples in terms ...
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Trakhtenbrot's Theorem in Coq: Finite Model Theory through the Constructive Lens
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. To showcase an application of Trakthenbrot's theorem, we continue our reduction chain with a manyone reduction from FSAT to separation logic. All our results are mechanised in the framework of a growing Coq library of synthetic undecidability proofs.
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