A Modal Defeasible Reasoner of Deontic Logic for the Semantic Web

2011 ◽  
Vol 7 (1) ◽  
pp. 18-43 ◽  
Author(s):  
Efstratios Kontopoulos ◽  
Nick Bassiliades ◽  
Guido Governatori ◽  
Grigoris Antoniou
Keyword(s):  
Modal Logic ◽  
Semantic Web ◽  
Deontic Logic ◽  
Expressive Power ◽  
Modal Logics ◽  
Cognitive State ◽  
Privacy Requirements ◽  
Defeasible Logic ◽  
Conflicting Information ◽  
Web Information

Defeasible logic is a non-monotonic formalism that deals with incomplete and conflicting information, whereas modal logic deals with the concepts of necessity and possibility. These types of logics play a significant role in the emerging Semantic Web, which enriches the available Web information with meaning, leading to better cooperation between end-users and applications. Defeasible and modal logics, in general, and, particularly, deontic logic provide means for modeling agent communities, where each agent is characterized by its cognitive profile and normative system, as well as policies, which define privacy requirements, access permissions, and individual rights. Toward this direction, this article discusses the extension of DR-DEVICE, a Semantic Web-aware defeasible reasoner, with a mechanism for expressing modal logic operators, while testing the implementation via deontic logic operators, concerned with obligations, permissions, and related concepts. The motivation behind this work is to develop a practical defeasible reasoner for the Semantic Web that takes advantage of the expressive power offered by modal logics, accompanied by the flexibility to define diverse agent behaviours. A further incentive is to study the various motivational notions of deontic logic and discuss the cognitive state of agents, as well as the interactions among them.

A Modal Defeasible Reasoner of Deontic Logic for the Semantic Web

Semantic Web ◽  
2013 ◽  
pp. 140-167
Author(s):  
Efstratios Kontopoulos ◽  
Nick Bassiliades ◽  
Guido Governatori ◽  
Grigoris Antoniou
Keyword(s):  
Modal Logic ◽  
Semantic Web ◽  
Deontic Logic ◽  
Expressive Power ◽  
Modal Logics ◽  
Cognitive State ◽  
Privacy Requirements ◽  
Defeasible Logic ◽  
Conflicting Information ◽  
Web Information

Defeasible logic is a non-monotonic formalism that deals with incomplete and conflicting information, whereas modal logic deals with the concepts of necessity and possibility. These types of logics play a significant role in the emerging Semantic Web, which enriches the available Web information with meaning, leading to better cooperation between end-users and applications. Defeasible and modal logics, in general, and, particularly, deontic logic provide means for modeling agent communities, where each agent is characterized by its cognitive profile and normative system, as well as policies, which define privacy requirements, access permissions, and individual rights. Toward this direction, this article discusses the extension of DR-DEVICE, a Semantic Web-aware defeasible reasoner, with a mechanism for expressing modal logic operators, while testing the implementation via deontic logic operators, concerned with obligations, permissions, and related concepts. The motivation behind this work is to develop a practical defeasible reasoner for the Semantic Web that takes advantage of the expressive power offered by modal logics, accompanied by the flexibility to define diverse agent behaviours. A further incentive is to study the various motivational notions of deontic logic and discuss the cognitive state of agents, as well as the interactions among them.

scholarly journals THE EXPRESSIVE POWER OF MEMORY LOGICS

2011 ◽  
Vol 4 (2) ◽  
pp. 290-318 ◽  
Author(s):  
CARLOS ARECES ◽  
DIEGO FIGUEIRA ◽  
SANTIAGO FIGUEIRA ◽  
SERGIO MERA
Keyword(s):  
Modal Logic ◽  
Expressive Power ◽  
Modal Logics ◽  
Hybrid Logic ◽  
Satisfiability Problem ◽  
Current Node

We investigate the expressive power of memory logics. These are modal logics extended with the possibility to store (or remove) the current node of evaluation in (or from) a memory, and to perform membership tests on the current memory. From this perspective, the hybrid logic ℋℒ (↓), for example, can be thought of as a particular case of a memory logic where the memory is an indexed list of elements of the domain.This work focuses in the case where the memory is a set, and we can test whether the current node belongs to the set or not. We prove that, in terms of expressive power, the memory logics we discuss here lie between the basic modal logic ${\cal K}$ and ℋℒ (↓). We show that the satisfiability problem of most of the logics we cover is undecidable. The only logic with a decidable satisfiability problem is obtained by imposing strong constraints on which elements can be memorized.

VISUAL MODELING OF DEFEASIBLE LOGIC RULES WITH DR-VisMo

2008 ◽  
Vol 17 (05) ◽  
pp. 903-924 ◽  
Author(s):  
EFSTRATIOS KONTOPOULOS ◽  
NICK BASSILIADES ◽  
GRIGORIS ANTONIOU ◽  
ANNA SERIDOU
Keyword(s):  
Semantic Web ◽  
Directed Graphs ◽  
Rule Base ◽  
Full Potential ◽  
Visualization System ◽  
Defeasible Logic ◽  
Conflicting Information ◽  
Rule Bases ◽  
Available Information ◽  
Logic Rule

The standardization of the Semantic Web has reached as far as ontologies and ontology languages. However, in order for the full potential of the Semantic Web to be achieved, the ability of reasoning over the available information is also essential. Rules can assist in this affair and various logics have been proposed for the Semantic Web domain. One of them is defeasible reasoning that deals with incomplete and conflicting information. However, despite its solid mathematical notation, it may be confusing to end users. To confront this downside, we proposed a representation schema for defeasible logic rule bases, which is based on directed graphs that feature distinct node and connection types. This paper presents DR-VisMo, a defeasible logic rule base editor and visualization system that implements this representation approach. The system also features a stratification algorithm for visualizing rule bases that deals with decisions, regarding the arrangement of the various elements in the graph. DR-VisMo is implemented as part of VDR-DEVICE, an environment for modeling and deploying defeasible logic rule bases on top of RDF ontologies.

scholarly journals Admissible Inference Rules and Semantic Property of Modal Logics

2021 ◽  
Vol 37 ◽  
pp. 104-117
Author(s):  
V.V. Rimatskiy ◽  
Keyword(s):  
Modal Logic ◽  
Inference Rule ◽  
Expressive Power ◽  
Modal Logics ◽  
Human Reasoning ◽  
Inference Rules ◽  
Semantic Property ◽  
Admissible Rule ◽  
Admissible Inference Rules ◽  
Deductive Power

Firstly semantic property of nonstandart logics were described by formulas which are peculiar to studied a models in general, and do not take to consideration a variable conditions and a changing assumptions. Evidently the notion of inference rule generalizes the notion of formulas and brings us more flexibility and more expressive power to model human reasoning and computing. In 2000-2010 a few results on describing of explicit bases for admissible inference rules for nonstandard logics (S4, K4, H etc.) appeared. The key property of these logics was weak co-cover property. Beside the improvement of deductive power in logic, an admissible rule are able to describe some semantic property of given logic. We describe a semantic property of modal logics in term of admissibility of given set of inference rules. We prove that modal logic over logic 𝐺𝐿 enjoys weak co-cover property iff all given rules are admissible for logic.

A Modal Semantics of Negation in Logic Programming

1992 ◽  
Vol 16 (3-4) ◽  
pp. 231-262
Author(s):  
Philippe Balbiani
Keyword(s):  
Modal Logic ◽  
Logic Programming ◽  
Modal Logics ◽  
Kripke Models ◽  
Logic Programs ◽  
Modal Semantics ◽  
Soundness And Completeness ◽  
Modal Completion ◽  
Well Foundedness

The beauty of modal logics and their interest lie in their ability to represent such different intensional concepts as knowledge, time, obligation, provability in arithmetic, … according to the properties satisfied by the accessibility relations of their Kripke models (transitivity, reflexivity, symmetry, well-foundedness, …). The purpose of this paper is to study the ability of modal logics to represent the concepts of provability and unprovability in logic programming. The use of modal logic to study the semantics of logic programming with negation is defended with the help of a modal completion formula. This formula is a modal translation of Clack’s formula. It gives soundness and completeness proofs for the negation as failure rule. It offers a formal characterization of unprovability in logic programs. It characterizes as well its stratified semantics.

scholarly journals Building an OWL ontology with Xper3

2018 ◽  
Vol 2 ◽  
pp. e25614 ◽  
Author(s):  
Florian Pellen ◽  
Sylvain Bouquin ◽  
Isabelle Mougenot ◽  
Régine Vignes-Lebbe
Keyword(s):  
Semantic Web ◽  
Knowledge Base ◽  
Expressive Power ◽  
Knowledge Bases ◽  
User Friendliness ◽  
Standard Format ◽  
Ontology Language ◽  
Closed World ◽  
Web Standards ◽  
Description Framework

Xper3 (Vignes Lebbe et al. 2016) is a collaborative knowledge base publishing platform that, since its launch in november 2013, has been adopted by over 2 thousand users (Pinel et al. 2017). This is mainly due to its user friendly interface and the simplicity of its data model. The data are stored in MySQL Relational DBs, but the exchange format uses the TDWG standard format SDD (Structured Descriptive DataHagedorn et al. 2005). However, each Xper3 knowledge base is a closed world that the author(s) may or may not share with the scientific community or the public via publishing content and/or identification key (Kopfstein 2016). The explicit taxonomic, geographic and phenotypic limits of a knowledge base are not always well defined in the metadata fields. Conversely terminology vocabularies, such as Phenotype and Trait Ontology PATO and the Plant Ontology PO, and software to edit them, such as Protégé and Phenoscape, are essential in the semantic web, but difficult to handle for biologist without computer skills. These ontologies constitute open worlds, and are expressed themselves by RDF triples (Resource Description Framework). Protégé offers vizualisation and reasoning capabilities for these ontologies (Gennari et al. 2003, Musen 2015). Our challenge is to combine the user friendliness of Xper3 with the expressive power of OWL (Web Ontology Language), the W3C standard for building ontologies. We therefore focused on analyzing the representation of the same taxonomic contents under Xper3 and under different models in OWL. After this critical analysis, we chose a description model that allows automatic export of SDD to OWL and can be easily enriched. We will present the results obtained and their validation on two knowledge bases, one on parasitic crustaceans (Sacculina) and the second on current ferns and fossils (Corvez and Grand 2014). The evolution of the Xper3 platform and the perspectives offered by this link with semantic web standards will be discussed.

scholarly journals Canonical formulas via locally finite reducts and generalized dualities

10.29007/hgbj ◽  
2018 ◽  
Author(s):  
Nick Bezhanishvili
Keyword(s):  
Modal Logic ◽  
Intuitionistic Logic ◽  
Algebraic Approach ◽  
Modal Logics ◽  
Substructural Logic ◽  
Locally Finite ◽  
Canonical Formulas

The method of canonical formulas is a powerful tool for investigating intuitionistic and modal logics. In this talk I will discuss an algebraic approach to this method. I will mostly concentrate on the case of intuitionistic logic. But I will also review the case of modal logic and possible generalizations to substructural logic.

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