2026· International Conference on Formal Structures for Computation and Deduction· pp. 24:1-24:17· 0 citations· 41 references
Computer Science
TL;DR
This paper provides a setting in which congruences can be treated as actual equalities, mirroring the informal practice of mathematicians and eliminating the need to use the lemmas typically required for formal congruence proofs.
This paper provides an expository comparison of two foundational proof systems in classical propositional logic: Gentzen's sequent calculus and Beth's semantic tableaux. Gentzen's sequent calculus is presented as a rule-based system built upon the single axiom $\alpha \Rightarrow \alpha$, whose key feature — the subfor...
We present a domain-theoretical formalization of interaction trees in the Rocq prover. Unlike existing formalizations, ours does not rely on Rocq's built-in coinduction. Hence, we avoid complications occurring in earlier works, such as artificially including silent steps to comply with Rocq's productivity checker, trea...
David Nowak, Vlad Rusu· Electronic Proceedings in Th...· 0 citations
GenZ is introduced, a generic theorem prover for sequent calculi implemented in Haskell that allows the user to specify a set of sequent rules, over which it performs proof search, and employs the zipper data structure.
Xiaoshuang Yang, Malvin Gattinger, Marianna Girlando et al.· 0 citations
We present an abstract framework for conservation and translation theorems between logical calculi. Unlike previous approaches, our setting does not require the underlying consequence relations to satisfy structural properties such as cut, allowing in particular for cut-free calculi. Moreover, we study translations bet...
It is shown that the epsilon calculus provides a natural framework for analyzing tolerance of falsity in proofs and for identifying conditions under which an incorrect proof can be semantically repaired.
The top-down solver TD is a generic fixpoint algorithm that can be used to compute partial post-solutions of equation systems for abstract interpretation. We consider two extensions of the TD to deal with infinite strictly ascending chains. For the TD extended with warrowing, we formally prove that it always returns pa...
Sarah Tilscher, Alexandra Graß, Helmut Seidl et al.· Journal of automated reasoni...· 0 citations
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