TY - GEN
T1 - Integrating Induction and Coinduction via Closure Operators and Proof Cycles
AU - Cohen, Liron
AU - Rowe, Reuben N.S.
N1 - Funding Information:
We are grateful to Alexandra Silva for valuable coinductive reasoning examples, and Juriaan Rot for helpful comments and pointers. We also extend thanks to the anonymous reviewers for their questions and comments.
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - Coinductive reasoning about infinitary data structures has many applications in computer science. Nonetheless developing natural proof systems (especially ones amenable to automation) for reasoning about coinductive data remains a challenge. This paper presents a minimal, generic formal framework that uniformly captures applicable (i.e. finitary) forms of inductive and coinductive reasoning in an intuitive manner. The logic extends transitive closure logic, a general purpose logic for inductive reasoning based on the transitive closure operator, with a dual ‘co-closure’ operator that similarly captures applicable coinductive reasoning in a natural, effective manner. We develop a sound and complete non-well-founded proof system for the extended logic, whose cyclic subsystem provides the basis for an effective system for automated inductive and coinductive reasoning. To demonstrate the adequacy of the framework we show that it captures the canonical coinductive data type: streams.
AB - Coinductive reasoning about infinitary data structures has many applications in computer science. Nonetheless developing natural proof systems (especially ones amenable to automation) for reasoning about coinductive data remains a challenge. This paper presents a minimal, generic formal framework that uniformly captures applicable (i.e. finitary) forms of inductive and coinductive reasoning in an intuitive manner. The logic extends transitive closure logic, a general purpose logic for inductive reasoning based on the transitive closure operator, with a dual ‘co-closure’ operator that similarly captures applicable coinductive reasoning in a natural, effective manner. We develop a sound and complete non-well-founded proof system for the extended logic, whose cyclic subsystem provides the basis for an effective system for automated inductive and coinductive reasoning. To demonstrate the adequacy of the framework we show that it captures the canonical coinductive data type: streams.
UR - http://www.scopus.com/inward/record.url?scp=85088235579&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-51074-9_21
DO - 10.1007/978-3-030-51074-9_21
M3 - Conference contribution
AN - SCOPUS:85088235579
SN - 9783030510732
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 375
EP - 394
BT - Automated Reasoning - 10th International Joint Conference, IJCAR 2020, Proceedings
A2 - Peltier, Nicolas
A2 - Sofronie-Stokkermans, Viorica
PB - Springer
T2 - 10th International Joint Conference on Automated Reasoning, IJCAR 2020
Y2 - 1 July 2020 through 4 July 2020
ER -