#### 76 Citations

Order-Sorted Reasoning in the Situation Calculus

- 2009

We propose a theory for reasoning about actions based on order-sorted predicate logic where one can consider an elab orate taxonomy of objects. We are interested in the projection problem: whether a… Expand

Report RR-90-10 Concept Logics

- 2019

Concept languages (as used in BACK, KL-ONE, KRYPTON, LOOM) are employed as knowledge representation formalisms in Artificial Intelligence. Their main purpose is to represent the generic concepts and… Expand

New Language Constructs and Inferences for the Knowledge Base Paradigm: A Business and Multi-agent Perspective ; Taaluitbreidingen en nieuwe inferenties voor het kennisbank paradigma vanuit een Business en Multi-Agent perspectief

- Computer Science
- 2016

This text uses an implementation of a KB system: the IDP system with corresponding language FO(·) to model challenging and interesting applications and proves the hypothesis that this approach has many advantages over standard declarative paradigms. Expand

Existential rigidity and many modalities in order-sorted logic

- Computer Science
- Knowl. Based Syst.
- 2011

In this study, a new labeled tableau calculus is presented to check the (un)satisfiability and validity of sorted modal formulas to extend order-sorted logic by introducing existential rigidity and many modalities. Expand

Finite domain and symbolic inference methods for extensions of first-order logic

- Computer Science, Mathematics
- AI Commun.
- 2011

This dissertation studies the tasks of constraint propagation, grounding, model revision, and debugging for FO(·), a rich extension of classical logic with, amongst others, inductive definitions and aggregates. Expand

The Typed Situation Calculus 2 Introduction

- 2011

We propose a theory for reasoning about actions based on order-so rt d predicate logic where one can consider an elaborate taxonomy of objects . We are interested in the projection problem: whether a… Expand

Distributed reasoning with ontologies and rules in order-sorted logic programming

- Computer Science
- J. Web Semant.
- 2009

A query-answering system that combines order-sorted linear resolution and rigid-property resolution as top-down algorithms to enable the reasoning to be effective and decidable. Expand

Translating a Dependently-Typed Logic to First-Order Logic

- Computer Science
- WADT
- 2008

A translation from DFOL to FOL formalized as an institution comorphism and show that it admits the model expansion property and implies the soundness of borrowing, which enables to reason about entailment in DFOL by using automated tools for FOL. Expand

A Unified Approach to Theory Reasoning

- Computer Science
- 2007

A classification for the various approaches for theory reasoning which is based on the syntactic concepts of literal level — term level — variable level is defined and current ways of equality handling are described. Expand

Combining Order-Sorted Logic Programming with Formal Ontology 1

- 2007

In formal ontology, entity types and relationships are philosophically defined, and the properties of objects are classified on the basis of sortality, rigidity, and identity (called property… Expand

#### References

SHOWING 1-6 OF 6 REFERENCES

On the Definition of 'Formal Deduction'

- Mathematics, Computer Science
- J. Symb. Log.
- 1956

One particular system E is to have the usual primitive symbols and formation rules of the pure first-order functional calculus, and the following formal axiom schemata and formal rules of inference. Expand

Logic of Many-Sorted Theories

- Mathematics, Computer Science
- J. Symb. Log.
- 1952

The purpose in this paper is to investigate the many-sorted systems and their elementary logics. Expand

Die Zulässigkeit der Behandlung mehrsortiger Theorien mittels der üblichen einsortigen Prädikatenlogik

- Mathematics
- 1951

The Completeness of the First-Order Functional Calculus

- Mathematics, Computer Science
- J. Symb. Log.
- 1949

This paper presents a new method of proof for the first-order functional calculus which requires less formal development of the system from the axioms and suggests a new approach to the problem of completeness for functional calculi of higher order. Expand