TY - GEN
T1 - On synthetic undecidability in Coq, with an application to the Entscheidungsproblem
AU - Forster, Yannick
AU - Kirst, Dominik
AU - Smolka, Gert
N1 - Publisher Copyright:
© 2019 ACM.
PY - 2019/1/14
Y1 - 2019/1/14
N2 - We formalise the computational undecidability of validity, satisfiability, and provability of first-order formulas following a synthetic approach based on the computation native to Coq's constructive type theory. Concretely, we consider Tarski and Kripke semantics as well as classical and intuitionistic natural deduction systems and provide compact many-one reductions from the Post correspondence problem (PCP). Moreover, developing a basic framework for synthetic computability theory in Coq, we formalise standard results concerning decidability, enumerability, and reducibility without reference to a concrete model of computation. For instance, we prove the equivalence of Post's theorem with Markov's principle and provide a convenient technique for establishing the enumerability of inductive predicates such as the considered proof systems and PCP.
AB - We formalise the computational undecidability of validity, satisfiability, and provability of first-order formulas following a synthetic approach based on the computation native to Coq's constructive type theory. Concretely, we consider Tarski and Kripke semantics as well as classical and intuitionistic natural deduction systems and provide compact many-one reductions from the Post correspondence problem (PCP). Moreover, developing a basic framework for synthetic computability theory in Coq, we formalise standard results concerning decidability, enumerability, and reducibility without reference to a concrete model of computation. For instance, we prove the equivalence of Post's theorem with Markov's principle and provide a convenient technique for establishing the enumerability of inductive predicates such as the considered proof systems and PCP.
KW - Coq
KW - Entscheidungsproblem
KW - Markov's principle
KW - Post's theorem
KW - first-order logic
KW - synthetic undecidability
UR - https://www.scopus.com/pages/publications/85061216624
U2 - 10.1145/3293880.3294091
DO - 10.1145/3293880.3294091
M3 - Conference contribution
AN - SCOPUS:85061216624
T3 - CPP 2019 - Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs, Co-located with POPL 2019
SP - 38
EP - 51
BT - CPP 2019 - Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs, Co-located with POPL 2019
A2 - Mahboubi, Assia
PB - Association for Computing Machinery, Inc
T2 - 8th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2019
Y2 - 14 January 2019 through 15 January 2019
ER -