TY - GEN
T1 - Combining deduction modulo and logics of fixed-point definitions
AU - Baelde, David
AU - Nadathur, Gopalan
PY - 2012
Y1 - 2012
N2 - Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of recursive specifications. These specifications are not directly complemented by fixed-point reasoning techniques and, correspondingly, do not have to satisfy strong monotonicity restrictions. We show how to incorporate a rewriting capability into logics of fixed-point definitions towards additionally supporting recursive specifications. Specifically, we describe a natural deduction calculus that adds a form of ''closed-world'' equality - -a key ingredient to supporting fixed-point definitions - -to deduction modulo, a framework for extending a logic with a rewriting layer operating on formulas. We show that our calculus enjoys strong normalizability when the rewrite system satisfies general properties and we demonstrate its usefulness in specifying and reasoning about syntax-based descriptions. Our integration of closed-world equality into deduction modulo is based on an elimination principle for this form of equality that, for the first time, allows us to require finiteness of proofs without sacrificing stability under reduction.
AB - Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of recursive specifications. These specifications are not directly complemented by fixed-point reasoning techniques and, correspondingly, do not have to satisfy strong monotonicity restrictions. We show how to incorporate a rewriting capability into logics of fixed-point definitions towards additionally supporting recursive specifications. Specifically, we describe a natural deduction calculus that adds a form of ''closed-world'' equality - -a key ingredient to supporting fixed-point definitions - -to deduction modulo, a framework for extending a logic with a rewriting layer operating on formulas. We show that our calculus enjoys strong normalizability when the rewrite system satisfies general properties and we demonstrate its usefulness in specifying and reasoning about syntax-based descriptions. Our integration of closed-world equality into deduction modulo is based on an elimination principle for this form of equality that, for the first time, allows us to require finiteness of proofs without sacrificing stability under reduction.
KW - closed-world equality
KW - deduction modulo
KW - fixed-point and recursive definitions
KW - strong normalizability
UR - http://www.scopus.com/inward/record.url?scp=84867178209&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84867178209&partnerID=8YFLogxK
U2 - 10.1109/LICS.2012.22
DO - 10.1109/LICS.2012.22
M3 - Conference contribution
AN - SCOPUS:84867178209
SN - 9780769547695
T3 - Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012
SP - 105
EP - 114
BT - Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012
T2 - 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012
Y2 - 25 June 2012 through 28 June 2012
ER -