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Decidable OrderSorted Logic Programming for Ontologies and Rules with Argument Restructuring
"... Abstract. This paper presents a decidable fragment for combining ontologies and rules in ordersorted logic programming. We describe ordersorted logic programming with sort, predicate, and metapredicate hierarchies for deriving predicate and metapredicate assertions. Metalevel predicates (predica ..."
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Abstract. This paper presents a decidable fragment for combining ontologies and rules in ordersorted logic programming. We describe ordersorted logic programming with sort, predicate, and metapredicate hierarchies for deriving predicate and metapredicate 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 ordersorted Hornclause calculus, we develop a queryanswering system that can answer queries such as atoms and metaatoms generalized by containing predicate variables. We show that the expressive queryanswering 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 OrderSorted 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 ordersorted logic programming. We describe ordersorted 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 ordersorted logic programming. We describe ordersorted logic programming with sort, predicate, and metapredicate hierarchies for deriving predicate and metapredicate 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 ordersorted Hornclause calculus, we develop a queryanswering system that can answer queries such as atoms and metaatoms generalized by containing predicate variables. We show that the expressive queryanswering 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 OrderSorted Logic
"... Ordersorted 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 sorthierarchy). However, this logic cannot represent more complex sorted expressions when they are true in any pos ..."
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Ordersorted 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 sorthierarchy). 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 ordersorted 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 ComputationTree Logic with Sequence Modal Operator ⋆
"... Abstract. In this paper, we propose a method for modeling concepts in full computationtree logic with sequence modal operators. An extended full computationtree 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 computationtree logic with sequence modal operators. An extended full computationtree 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 modelchecking problems of CTLS ∗ are shown to be decidable. An illustrative example of biological taxonomy is presented using CTLS ∗ formulas. 1
SequenceIndexed LinearTime 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, sequenceindexed lineartime temporal logic (SLTL), is obtained semantically from standard lineartime 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, sequenceindexed lineartime temporal logic (SLTL), is obtained semantically from standard lineartime 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 Gentzentype sequent calculus for SLTL is introduced, and the completeness and cutelimination theorems for it are proved. SLTL is also shown to be PSPACEcomplete 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 ordersorted temposituational logic (OSTSL) with rigid/antirigid 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 ordersorted temposituational logic (OSTSL) with rigid/antirigid sorts and an existential predicate. In this logic, rigid/antirigid 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 temposituational formulas are logically valid. key words: formal ontology, semantic web, ordersorted logic 1.
An OrderSorted Query System for Sort, Predicate, and MetaPredicate Hierarchies
"... Abstract. This paper presents a decidable ordersorted query system for reasoning between ontologies (in OWL) and rules (in RuleML). We describe an ordersorted language with sort, predicate, and metapredicate hierarchies for deriving predicate and metapredicate assertions. Metalevel predicates (p ..."
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Abstract. This paper presents a decidable ordersorted query system for reasoning between ontologies (in OWL) and rules (in RuleML). We describe an ordersorted language with sort, predicate, and metapredicate hierarchies for deriving predicate and metapredicate 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 ordersorted Hornclause calculus, we develop a queryanswering system that can answer queries such as atoms and metaatoms generalized by containing predicate variables. We show that the expressive queryanswering system computes every generalized query in single exponential time, i.e., the complexity of our query system is equal to that of DATALOG. 1