TY - UNPB
T1 - Infinitary and Cyclic Proof Systems for Transitive Closure Logic
AU - Cohen, Liron
AU - Rowe, Reuben N. S.
PY - 2018/6/28
Y1 - 2018/6/28
N2 - Transitive closure logic is a known extension of first-order logic obtained
by introducing a transitive closure operator. While other extensions of
first-order logic with inductive definitions are a priori parametrized by a set
of inductive definitions, the addition of the transitive closure operator
uniformly captures all finitary inductive definitions. In this paper we present
an infinitary proof system for transitive closure logic which is an infinite
descent-style counterpart to the existing (explicit induction) proof system for
the logic. We show that, as for similar systems for first-order logic with
inductive definitions, our infinitary system is complete for the standard
semantics and subsumes the explicit system. Moreover, the uniformity of the
transitive closure operator allows semantically meaningful complete
restrictions to be defined using simple syntactic criteria. Consequently, the
restriction to regular infinitary (i.e. cyclic) proofs provides the basis for
an effective system for automating inductive reasoning
AB - Transitive closure logic is a known extension of first-order logic obtained
by introducing a transitive closure operator. While other extensions of
first-order logic with inductive definitions are a priori parametrized by a set
of inductive definitions, the addition of the transitive closure operator
uniformly captures all finitary inductive definitions. In this paper we present
an infinitary proof system for transitive closure logic which is an infinite
descent-style counterpart to the existing (explicit induction) proof system for
the logic. We show that, as for similar systems for first-order logic with
inductive definitions, our infinitary system is complete for the standard
semantics and subsumes the explicit system. Moreover, the uniformity of the
transitive closure operator allows semantically meaningful complete
restrictions to be defined using simple syntactic criteria. Consequently, the
restriction to regular infinitary (i.e. cyclic) proofs provides the basis for
an effective system for automating inductive reasoning
KW - Computer Science - Logic in Computer Science
KW - F.3.1
KW - F.4.1
U2 - 10.48550/arXiv.1802.00756
DO - 10.48550/arXiv.1802.00756
M3 - Preprint
BT - Infinitary and Cyclic Proof Systems for Transitive Closure Logic
ER -