Towards a general theory of action and time
Artificial Intelligence
A mechanical solution of Schubert's steamroller by many-sorted resolution
Artificial Intelligence
Logic for computer science: foundations of automatic theorem proving
Logic for computer science: foundations of automatic theorem proving
Login: A logic programming language with built-in inheritance
Journal of Logic Programming
The mathematics of inheritance systems
The mathematics of inheritance systems
A more expressive formulation of many sorted logic
Journal of Automated Reasoning
Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
A many-sorted calculus based on resolution and paramodulation
A many-sorted calculus based on resolution and paramodulation
Journal of the ACM (JACM)
Proceedings of the workshop on Sorts and types in artificial intelligence
Computational aspects of an order-sorted logic with term declarations
Computational aspects of an order-sorted logic with term declarations
The substitutional framework for sorted deduction: fundamental results on hybrid reasoning
Artificial Intelligence - Special issue on knowledge representation
The logic of typed feature structures
The logic of typed feature structures
An order-sorted logic for knowledge representation systems
Artificial Intelligence
Feature-constraint logics for unification grammars
Journal of Logic Programming
Types in logic programming
Introduction to many-sorted logic
Many-sorted logic and its applications
Logical foundations of object-oriented and frame-based languages
Journal of the ACM (JACM)
New HELIC-II: a software tool for legal reasoning
ICAIL '95 Proceedings of the 5th international conference on Artificial intelligence and law
Inheritance theory: an artificial intelligence approach
Inheritance theory: an artificial intelligence approach
From logic programming to Prolog
From logic programming to Prolog
An order-sorted resolution in theory and practice
Theoretical Computer Science - Special issue: theoretical computer science in Australia and New Zealand
Logical approaches to incomplete information: a survey
Logics for databases and information systems
Event, property and hierarchy in order-sorted logic
Proceedings of the 1999 international conference on Logic programming
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
From Logic to Logic Programming
From Logic to Logic Programming
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
An Order-Sorted Resolution with Implicitly Negative Sorts
Proceedings of the 17th International Conference on Logic Programming
The completeness of logic programming with sort predicates
Systems and Computers in Japan
Logical aspects of events: quantification, sorts, composition and disjointness
AOW '05 Proceedings of the 2005 Australasian Ontology Workshop - Volume 58
A hybrid reasoning system for terminologies and first-order clauses in knowledge bases
New Generation Computing
Semantic enrichment in ontologies for matching
AOW '06 Proceedings of the second Australasian workshop on Advances in ontologies - Volume 72
An Ontology Formalization of Relation Type Hierarchy in Conceptual Structure Theory
AI '08 Proceedings of the 21st Australasian Joint Conference on Artificial Intelligence: Advances in Artificial Intelligence
Decidable Order-Sorted Logic Programming for Ontologies and Rules with Argument Restructuring
ISWC '09 Proceedings of the 8th International Semantic Web Conference
Meta-relation and ontology closure in conceptual structure theory
Artificial Intelligence and Law
An upper ontology for event classifications and relations
AI'07 Proceedings of the 20th Australian joint conference on Advances in artificial intelligence
Automatic coding rule conformance checking using logic programming
PADL'08 Proceedings of the 10th international conference on Practical aspects of declarative languages
Existential rigidity and many modalities in order-sorted logic
Knowledge-Based Systems
An order-sorted quantified modal logic for meta-ontology
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Reasoning about Resources and Information: A Linear Logic Approach
Fundamenta Informaticae
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Order-sorted logic has been formalized as first-order logic with sorted terms where sorts are ordered to build a hierarchy (called a sort-hierarchy). These sorted logics lead to useful expressions and inference methods for structural knowledge that ordinary first-order logic lacks. Nitta et al. pointed out that for legal reasoning a sort-hierarchy (or a sorted term) is not sufficient to describe structural knowledge for event assertions, which express facts caused at some particular time and place. The event assertions are represented by predicates with n arguments (i.e., n-ary predicates), and then a particular kind of hierarchy (called a predicate hierarchy) is built by a relationship among the predicates. To deal with such a predicate hierarchy, which is more intricate than a sort-hierarchy, Nitta et al. implemented a typed (sorted) logic programming language extended to include a hierarchy of verbal concepts (corresponding to predicates). However, the inference system lacks a theoretical foundation because its hierarchical expressions exceed the formalization of order-sorted logic. In this paper, we formalize a logic programming language with not only a sort-hierarchy but also a predicate hierarchy. This language can derive general and concrete expressions in the two kinds of hierarchies. For the hierarchical reasoning of predicates, we propose a manipulation of arguments in which surplus and missing arguments in derived predicates are eliminated and supplemented. As discussed by Allen, McDermott and Shoham in research on temporal logic and as applied by Nitta et al. to legal reasoning, if each predicate is interpreted as an event or action (not as a static property), then missing arguments should be supplemented by existential terms in the argument manipulation. Based on this, we develop a Horn clause resolution system extended to add inference rules of predicate hierarchies. With a semantic model restricted by interpreting a predicate hierarchy, the soundness and completeness of the Horn-clause resolution is proven.