1,499 research outputs found
On Equivalence of Infinitary Formulas under the Stable Model Semantics
Propositional formulas that are equivalent in intuitionistic logic, or in its
extension known as the logic of here-and-there, have the same stable models. We
extend this theorem to propositional formulas with infinitely long conjunctions
and disjunctions and show how to apply this generalization to proving
properties of aggregates in answer set programming. To appear in Theory and
Practice of Logic Programming (TPLP)
A computability theoretic equivalent to Vaught's conjecture
We prove that, for every theory which is given by an sentence, has less than many countable
models if and only if we have that, for every on a cone of
Turing degrees, every -hyperarithmetic model of has an -computable
copy. We also find a concrete description, relative to some oracle, of the
Turing-degree spectra of all the models of a counterexample to Vaught's
conjecture
Proving Looping and Non-Looping Non-Termination by Finite Automata
A new technique is presented to prove non-termination of term rewriting. The
basic idea is to find a non-empty regular language of terms that is closed
under rewriting and does not contain normal forms. It is automated by
representing the language by a tree automaton with a fixed number of states,
and expressing the mentioned requirements in a SAT formula. Satisfiability of
this formula implies non-termination. Our approach succeeds for many examples
where all earlier techniques fail, for instance for the S-rule from combinatory
logic
On Hanf numbers of the infinitary order property
We study several cardinal, and ordinal--valued functions that are relatives
of Hanf numbers. Let kappa be an infinite cardinal, and let T subseteq
L_{kappa^+, omega} be a theory of cardinality <= kappa, and let gamma be an
ordinal >= kappa^+. For example we look at (1) mu_{T}^*(gamma, kappa):= min
{mu^* for all phi in L_{infinity, omega}, with rk(phi)< gamma, if T has the
(phi, mu^*)-order property then there exists a formula phi'(x;y) in L_{kappa^+,
omega}, such that for every chi >= kappa, T has the (phi', chi)-order
property}; and (2) mu^*(gamma, kappa):= sup{mu_T^*(gamma, kappa)| T in
L_{kappa^+,omega}}
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