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pro vyhledávání: '"Hetzl, Stefan"'
Autor:
Hetzl, Stefan, Jalali, Raheleh
Craig interpolation is a fundamental property of classical and non-classic logics with a plethora of applications from philosophical logic to computer-aided verification. The question of which interpolants can be obtained from an interpolation algori
Externí odkaz:
http://arxiv.org/abs/2402.02829
Autor:
Hetzl, Stefan, Vierling, Jannik
We investigate quantifier-free induction for Lisp-like lists constructed inductively from the empty list $\mathit{nil}$ and the operation $\mathit{cons}$, that adds an element to the front of a list. First we show that, for $m \geq 1$, quantifier-fre
Externí odkaz:
http://arxiv.org/abs/2305.08682
Autor:
Hetzl, Stefan, Vierling, Jannik
The notion of clause set cycle abstracts a family of methods for automated inductive theorem proving based on the detection of cyclic dependencies between clause sets. By discerning the underlying logical features of clause set cycles, we are able to
Externí odkaz:
http://arxiv.org/abs/2110.03246
Autor:
Hetzl, Stefan, Kloibhofer, Johannes
Publikováno v:
EPTCS 344, 2021, pp. 65-78
We consider constrained Horn clause solving from the more general point of view of solving formula equations. Constrained Horn clauses correspond to the subclass of Horn formula equations. We state and prove a fixed-point theorem for Horn formula equ
Externí odkaz:
http://arxiv.org/abs/2109.04633
Autor:
Hetzl, Stefan, Vierling, Jannik
We consider a typical integration of induction in saturation-based theorem provers and investigate the effects of Skolem symbols occurring in the induction formulas. In a practically relevant setting we establish a Skolem-free characterization of ref
Externí odkaz:
http://arxiv.org/abs/2105.07734
Autor:
Hetzl, Stefan, Vierling, Jannik
Publikováno v:
Logical Methods in Computer Science, Volume 16, Issue 4 (November 30, 2020) lmcs:5832
In this article we relate a family of methods for automated inductive theorem proving based on cycle detection in saturation-based provers to well-known theories of induction. To this end we introduce the notion of clause set cycles -- a formalism ab
Externí odkaz:
http://arxiv.org/abs/1910.03917
Publikováno v:
Math. Struct. Comp. Sci. 29 (2019) 1009-1029
Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view, it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information of which instances have been
Externí odkaz:
http://arxiv.org/abs/1802.08076
Autor:
Hetzl, Stefan, Vierling, Jannik
Publikováno v:
In Theoretical Computer Science 31 October 2022 935:21-46
We describe a new cognitive ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions. Furthermore, we present an initial (first-order) formalization of this mechanism together w
Externí odkaz:
http://arxiv.org/abs/1710.04022
Autor:
Hetzl, Stefan, Wong, Tin Lok
Publikováno v:
Logical Methods in Computer Science, Volume 13, Issue 4, Automated deduction (April 13, 2018) lmcs:3256
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a goal. Based
Externí odkaz:
http://arxiv.org/abs/1704.01930