Abstract. UML class diagrams (UCDs) are the de-facto standard formalism for the analysis and design of information systems. By adopting formal language techniques to capture constraints expressed by UCDs one can exploit automated reasoning tools to detect relevant properties, such as schema and class satisfiability and subsumption between classes. Among the reasoning tasks of interest, the basic one is detecting full satisfiability of a diagram, i.e., whether there exists an instantiation of the diagram where all classes and associations of the diagram are non-empty and all the constraints of the diagram are respected. In this paper we establish tight complexity results for full satisfiability for various fragments of UML class diagrams. This investigation shows that the full satisfiability problem is ExpTime-complete in the full scenario, NP-complete if we drop isa between relationships, and NLogSpace-complete if we further drop covering over classes. 1

It is known that paraconsistent logical systems are more appropriate for inconsistency-tolerant and uncertainty reasoning than other types of logical systems. In this paper, a paraconsistent computation tree logic, PCTL, is obtained by adding paraconsistent negation to the standard computation tree logic CTL. PCTL can be used to appropriately formalize inconsistency-tolerant temporal reasoning. A theorem for embedding PCTL into CTL is proved. The validity, satisfiability, and model-checking problems of PCTL are shown to be decidable. The embedding and decidability results indicate that we can reuse the existing CTL-based algorithms for validity, satisfiability, and model-checking. An illustrative example of medical reasoning involving the use of PCTL is presented.

Order-sorted logic is a useful tool for knowledge representation and reasoning because it enables representation of sorted terms and formulas along with partially ordered sorts (called sort-hierarchy). However, this logic cannot represent more complex sorted expressions when they are true in any possible world (as rigid) or some possible worlds (as modality) such as time, space, belief, or situation. In this study, we extend order-sorted logic by introducing existential rigidity and many modalities. In the extended logic, sorted modal formulas are interpreted over the Cartesian product of sets of possible worlds. We present a new labeled tableau calculus to check the (un)satisfiability and validity of sorted modal formulas. 1

Abstract. This paper presents a decidable order-sorted query system for reasoning between ontologies (in OWL) and rules (in RuleML). We describe an order-sorted language with sort, predicate, and meta-predicate hierarchies for deriving predicate and meta-predicate assertions. Metalevel 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 queryanswering system 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, i.e., the complexity of our query system is equal to that of DATALOG. 1

Abstract It is known that paraconsistent logical systems are more appropriate for inconsistency-tolerant and uncertainty reasoning than other types of logical systems. In this paper, a paraconsistent computation tree logic, PCTL, is obtained by adding paraconsistent negation to the standard computation tree logic CTL. PCTL can be used to appropriately formalize inconsistency-tolerant temporal reasoning. A theorem for embedding PCTL into CTL is proved. The validity, satisfiability, and model-checking problems of PCTL are shown to be decidable. The embedding and decidability results indicate that we can reuse the existing CTL-based algorithms for validity, satisfiability, and model-checking. An illustrative example of medical reasoning involving the use of PCTL is presented.

Abstract. In this paper, we propose a method for modeling concepts in full computation-tree logic with sequence modal operators. An extended full computation-tree logic, CTLS ∗ , is introduced as a Kripke semantics with a sequence modal operator. This logic can appropriately represent hierarchical tree structures in cases where sequence modal operators in CTLS ∗ are applied to tree structures. We prove a theorem for embedding CTLS ∗ into CTL ∗. The validity, satisfiability, and model-checking problems of CTLS ∗ are shown to be decidable. An illustrative example of biological taxonomy is presented using CTLS ∗ formulas. 1

In this paper, we propose a proof system for reasoning on certain specifications of secure authentication systems. For this purpose, a new logic, sequence-indexed linear-time temporal logic (SLTL), is obtained semantically from standard linear-time temporal logic (LTL) by adding a sequence modal operator that represents a sequence of symbols. By this sequence modal operator, we can appropriately express message flows between clients and servers and states of servers in temporal reasoning. A Gentzen-type sequent calculus for SLTL is introduced, and the completeness and cut-elimination theorems for it are proved. SLTL is also shown to be PSPACE-complete and embeddable into LTL.