[Show abstract][Hide abstract] ABSTRACT: We investigate the problem of deciding first-order theories of finite trees with several distinguished congruence relations, each of them given by some equational axioms. We give an automata-based solution for the case where the different equational axiom systems are linear and variable-disjoint (this includes the case where all axioms are ground), and where the logic does not permit to express tree relations x=f(y,z). We show that the problem is undecidable when these restrictions are relaxed. As motivation and application, we show how to translate the model checking problem of ApiL, a spatial equational logic for the applied pi-calculus, to the validity of first-order formulas in term algebras with multiple congruence relations.
[Show abstract][Hide abstract] ABSTRACT: The existential fragment of the first-order theory of the "recursive path or- dering" (with multiset and lexicographic "status") is decidable when the precedence on function symbols is total (Com90, JO91), but is undecid- able for arbitrary formulas. Is the existential fragment decidable for partial precedences?
[Show abstract][Hide abstract] ABSTRACT: This paper presents a decidable order-sorted query system for reasoning between ontologies and rules. We describe order-sorted logic programming with sort, predicate, and meta-predicate hierarchies (OSL3h), which derives predicate and meta-predicate assertions. Meta-level predicates (predicates of predicates) are useful for representing relationships between predicate formulas, and further, they conceptually yield a hierarchy similar to the hierarchies of sorts and predicates. By extending the order-sorted Horn-clause calculus, we develop a query-answering system in OSL3h that can answer queries such as atoms and meta-atoms generalized by containing predicate variables. We show that the expressive query-answering system computes every generalized query in single exponential time, that is, the complexity of our query system is equal to that of DATALOG.
Knowledge and Information Systems 35(2). · 2.23 Impact Factor
Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.