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Decidable Order-Sorted Logic Programming for Ontologies and Rules with Argument Restructuring
"... Abstract. This paper presents a decidable fragment for combining ontologies and rules in order-sorted logic programming. We describe ordersorted logic programming with sort, predicate, and meta-predicate hierarchies for deriving predicate and meta-predicate assertions. Meta-level predicates (predica ..."
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Abstract. This paper presents a decidable fragment for combining ontologies and rules in order-sorted logic programming. We describe ordersorted logic programming with sort, predicate, and meta-predicate hierarchies for deriving 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 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
The Decidability and Complexity of Order-Sorted Logic Programming for Ontologies and Rules with Argument Restructuring
"... Abstract. Decidable reasoning between ontologies and rules is required for the Semantic Web. This paper presents a decidable fragment for combining ontologies and rules in order-sorted logic programming. We describe order-sorted logic programming with sort, predicate, and metapredicate hierarchies f ..."
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Abstract. Decidable reasoning between ontologies and rules is required for the Semantic Web. This paper presents a decidable fragment for combining ontologies and rules in order-sorted logic programming. We describe order-sorted logic programming with sort, predicate, and metapredicate hierarchies for deriving 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 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
Existential Rigidity and Many Modalities in Order-Sorted Logic
"... 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 pos ..."
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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
Conceptual Modeling in Full Computation-Tree Logic with Sequence Modal Operator ⋆
"... 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 t ..."
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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
Sequence-Indexed Linear-Time Temporal Logic: Proof System and Application ∗
"... 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 ope ..."
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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.
1 PAPER A Time and Situation Dependent Semantics for Ontological Property Classification ∗
"... This paper proposes a new semantics that characterizes the time and/or situation dependencies of properties, together with the ontological notion of existential rigidity. For this purpose, we present order-sorted tempo-situational logic (OSTSL) with rigid/anti-rigid sorts and an existential predicat ..."
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This paper proposes a new semantics that characterizes the time and/or situation dependencies of properties, together with the ontological notion of existential rigidity. For this purpose, we present order-sorted tempo-situational logic (OSTSL) with rigid/anti-rigid sorts and an existential predicate. In this logic, rigid/anti-rigid sorted terms enable the expressions for sortal properties, and temporal and situational operators suitably represent the ontological axioms of existential rigidity and time and/or situation dependencies. A specific semantics of OSTSL adheres to the temporal and situational behaviors of properties based on existential rigidity. As a result, the semantics guarantees that the ontological axioms of properties expressed by sorted tempo-situational formulas are logically valid. key words: formal ontology, semantic web, order-sorted logic 1.
An Order-Sorted Query System for Sort, Predicate, and Meta-Predicate Hierarchies
"... 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 (p ..."
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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
