TY - GEN
T1 - Completeness for Ancestral Logic via a Computationally-Meaningful Semantics
AU - Cohen, Liron
N1 - Publisher Copyright: © Springer International Publishing AG 2017.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - First-order logic (FOL) is evidently insufficient for the many applications of logic in computer science, mainly due to its inability to provide inductive definitions. Therefore, only an extension of FOL which allows finitary inductive definitions can be used as a framework for automated reasoning. The minimal logic that is suitable for this goal is Ancestral Logic (AL), which is an extension of FOL by a transitive closure operator. In order for AL to be able to serve as a reasonable (and better) substitute to the use of FOL in computer science, it is crucial to develop adequate, user-friendly proof systems for it. While the expressiveness of AL renders any effective proof system for it incomplete with respect to the standard semantics, there are useful approximations. In this paper we show that such a Gentzen-style approximation is both sound and complete with respect to a natural, computationally-meaningful Henkin-style semantics for AL.
AB - First-order logic (FOL) is evidently insufficient for the many applications of logic in computer science, mainly due to its inability to provide inductive definitions. Therefore, only an extension of FOL which allows finitary inductive definitions can be used as a framework for automated reasoning. The minimal logic that is suitable for this goal is Ancestral Logic (AL), which is an extension of FOL by a transitive closure operator. In order for AL to be able to serve as a reasonable (and better) substitute to the use of FOL in computer science, it is crucial to develop adequate, user-friendly proof systems for it. While the expressiveness of AL renders any effective proof system for it incomplete with respect to the standard semantics, there are useful approximations. In this paper we show that such a Gentzen-style approximation is both sound and complete with respect to a natural, computationally-meaningful Henkin-style semantics for AL.
UR - http://www.scopus.com/inward/record.url?scp=85029504609&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-319-66902-1_15
DO - https://doi.org/10.1007/978-3-319-66902-1_15
M3 - Conference contribution
SN - 9783319669014
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 247
EP - 260
BT - Automated Reasoning with Analytic Tableaux and Related Methods - 26th International Conference, TABLEAUX 2017, Proceedings
A2 - Nalon, Claudia
A2 - Schmidt, Renate A.
PB - Springer Verlag
T2 - 26th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2017
Y2 - 25 September 2017 through 28 September 2017
ER -