Knowledge Representation and Reasoning Research Publications

2020

Paterson-Jones G, Casini G, Meyer T. BKLM - An expressive logic for defeasible reasoning. 18th International Workshop on Non-Monotonic Reasoning. 2020.

Propositional KLM-style defeasible reasoning involves a core propositional logic capable of expressing defeasible (or conditional) implications. The semantics for this logic is based on Kripke-like structures known as ranked interpretations. KLM-style defeasible entailment is referred to as rational whenever the defeasible entailment relation under consideration generates a set of defeasible implications all satisfying a set of rationality postulates known as the KLM postulates. In a recent paper Booth et al. proposed PTL, a logic that is more expressive than the core KLM logic. They proved an impossibility result, showing that defeasible entailment for PTL fails to satisfy a set of rationality postulates similar in spirit to the KLM postulates. Their interpretation of the impossibility result is that defeasible entailment for PTL need not be unique. In this paper we continue the line of research in which the expressivity of the core KLM logic is extended. We present the logic Boolean KLM (BKLM) in which we allow for disjunctions, conjunctions, and negations, but not nesting, of defeasible implications. Our contribution is twofold. Firstly, we show (perhaps surprisingly) that BKLM is more expressive than PTL. Our proof is based on the fact that BKLM can characterise all single ranked interpretations, whereas PTL cannot. Secondly, given that the PTL impossibility result also applies to BKLM, we adapt the different forms of PTL entailment proposed by Booth et al. to apply to BKLM.

@misc{383,
  author = {Guy Paterson-Jones and Giovanni Casini and Thomas Meyer},
  title = {BKLM - An expressive logic for defeasible reasoning},
  abstract = {Propositional KLM-style defeasible reasoning involves a core propositional logic capable of expressing defeasible (or conditional) implications. The semantics for this logic is based on Kripke-like structures known as ranked interpretations. KLM-style defeasible entailment is referred to as rational whenever the defeasible entailment relation under consideration generates a set of defeasible implications all satisfying a set of rationality postulates known as the KLM postulates. In a recent paper Booth et al. proposed PTL, a logic that is more expressive than the core KLM logic. They proved an impossibility result, showing that defeasible entailment for PTL fails to satisfy a set of rationality postulates similar in spirit to the KLM postulates. Their interpretation of the impossibility result is that defeasible entailment for PTL need not be unique.
In this paper we continue the line of research in which the expressivity of the core KLM logic is extended. We present the logic Boolean KLM (BKLM) in which we allow for disjunctions, conjunctions, and negations, but not nesting, of defeasible implications. Our contribution is twofold. Firstly, we show (perhaps surprisingly) that BKLM is more expressive than PTL. Our proof is based on the fact that BKLM can characterise all single ranked interpretations, whereas PTL cannot. Secondly, given that the PTL impossibility result also applies to BKLM, we adapt the different forms of PTL entailment proposed by Booth et al. to apply to BKLM.},
  year = {2020},
  journal = {18th International Workshop on Non-Monotonic Reasoning},
  month = {12/09/2020},
}
Casini G, Meyer T, Varzinczak I. Rational Defeasible Belief Change. In: 17th International Conference on Principles of Knowledge Representation and Reasoning (KR 2020). Virtual: IJCAI; 2020. doi:10.24963/kr.2020/22.

We present a formal framework for modelling belief change within a non-monotonic reasoning system. Belief change and non-monotonic reasoning are two areas that are formally closely related, with recent attention being paid towards the analysis of belief change within a non-monotonic environment. In this paper we consider the classical AGM belief change operators, contraction and revision, applied to a defeasible setting in the style of Kraus, Lehmann, and Magidor. The investigation leads us to the formal characterisation of a number of classes of defeasible belief change operators. For the most interesting classes we need to consider the problem of iterated belief change, generalising the classical work of Darwiche and Pearl in the process. Our work involves belief change operators aimed at ensuring logical consistency, as well as the characterisation of analogous operators aimed at obtaining coherence—an important notion within the field of logic-based ontologies

@{382,
  author = {Giovanni Casini and Thomas Meyer and Ivan Varzinczak},
  title = {Rational Defeasible Belief Change},
  abstract = {We present a formal framework for modelling belief change within a non-monotonic reasoning system. Belief change and non-monotonic reasoning are two areas that are formally closely related, with recent attention being paid towards the analysis of belief change within a non-monotonic environment. In this paper we consider the classical AGM belief change operators, contraction and revision, applied to a defeasible setting in the style of Kraus, Lehmann, and Magidor. The investigation leads us to the formal characterisation of a number of classes of defeasible belief change operators. For the most interesting classes we need to consider the problem of iterated belief change, generalising the classical work of Darwiche and Pearl in the process. Our work involves belief change operators aimed at ensuring logical consistency, as well as the characterisation of analogous operators aimed at obtaining coherence—an important notion within the field of logic-based ontologies},
  year = {2020},
  journal = {17th International Conference on Principles of Knowledge Representation and Reasoning (KR 2020)},
  pages = {213-222},
  month = {12/09/2020},
  publisher = {IJCAI},
  address = {Virtual},
  url = {https://library.confdna.com/kr/2020/},
  doi = {10.24963/kr.2020/22},
}
Moodley D, Meyer T. Artificial Intelligence – Where it is heading and what we should do about it . 2020. https://link.springer.com/article/10.1007/s42354-020-0269-5.

Artificial Intelligence (AI) is already shaping our everyday lives. While there is enormous potential for harnessing AI to solve complex industrial and social problems and to create new and innovative products and solutions, many organisations are still grappling to understand the relevance and future impact of AI on their activities and what they should be doing about it.

@misc{381,
  author = {Deshen Moodley and Thomas Meyer},
  title = {Artificial Intelligence – Where it is heading and what we should do about it},
  abstract = {Artificial Intelligence (AI) is already shaping our everyday lives. While there is enormous potential for harnessing AI to solve complex industrial and social problems and to create new and innovative products and solutions, many organisations are still grappling to understand the relevance and future impact of AI on their activities and what they should be doing about it.},
  year = {2020},
  url = {https://link.springer.com/article/10.1007/s42354-020-0269-5},
}

2019

Britz K, Casini G, Meyer T, Varzinczak I. A KLM Perspective on Defeasible Reasoning for Description Logics. In: Description Logic, Theory Combination, and All That. Switzerland: Springer; 2019. doi:https://doi.org/10.1007/978-3-030-22102-7 _ 7.

In this paper we present an approach to defeasible reasoning for the description logic ALC. The results discussed here are based on work done by Kraus, Lehmann and Magidor (KLM) on defeasible conditionals in the propositional case. We consider versions of a preferential semantics for two forms of defeasible subsumption, and link these semantic constructions formally to KLM-style syntactic properties via representation results. In addition to showing that the semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. With the semantics of the defeasible version of ALC in place, we turn to the investigation of an appropriate form of defeasible entailment for this enriched version of ALC. This investigation includes an algorithm for the computation of a form of defeasible entailment known as rational closure in the propositional case. Importantly, the algorithm relies completely on classical entailment checks and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of the underlying classical ALC. Before concluding, we take a brief tour of some existing work on defeasible extensions of ALC that go beyond defeasible subsumption.

@inbook{240,
  author = {Katarina Britz and Giovanni Casini and Thomas Meyer and Ivan Varzinczak},
  title = {A KLM Perspective on Defeasible Reasoning for Description Logics},
  abstract = {In this paper we present an approach to defeasible reasoning for the description logic ALC. The results discussed here are based on work done by Kraus, Lehmann and Magidor (KLM) on defeasible conditionals in the propositional case. We consider versions of a preferential semantics for two forms of defeasible subsumption, and link these semantic constructions formally to KLM-style syntactic properties via representation results. In addition to showing that the semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. With the semantics of the defeasible version of ALC in place, we turn to the investigation of an appropriate form of defeasible entailment for this enriched version of ALC. This investigation includes an algorithm for the computation of a form of defeasible entailment known as rational closure in the propositional case. Importantly, the algorithm relies completely on classical entailment checks and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of the underlying classical ALC. Before concluding, we take a brief tour of some existing work on defeasible extensions of ALC that go beyond defeasible subsumption.},
  year = {2019},
  journal = {Description Logic, Theory Combination, and All That},
  pages = {147–173},
  publisher = {Springer},
  address = {Switzerland},
  isbn = {978-3-030-22101-0},
  url = {https://link.springer.com/book/10.1007%2F978-3-030-22102-7},
  doi = {https://doi.org/10.1007/978-3-030-22102-7 _ 7},
}
Casini G, Meyer T, Varzinczak I. Taking Defeasible Entailment Beyond Rational Closure. In: European Conference on Logics in Artificial Intelligence. Switzerland: Springer; 2019. doi:https://doi.org/10.1007/978-3-030-19570-0 _ 12.

We present a systematic approach for extending the KLM framework for defeasible entailment. We first present a class of basic defeasible entailment relations, characterise it in three distinct ways and provide a high-level algorithm for computing it. This framework is then refined, with the refined version being characterised in a similar manner. We show that the two well-known forms of defeasible entailment, rational closure and lexicographic closure, fall within our refined framework, that rational closure is the most conservative of the defeasible entailment relations within the framework (with respect to subset inclusion), but that there are forms of defeasible entailment within our framework that are more “adventurous” than lexicographic closure.

@{238,
  author = {Giovanni Casini and Thomas Meyer and Ivan Varzinczak},
  title = {Taking Defeasible Entailment Beyond Rational Closure},
  abstract = {We present a systematic approach for extending the KLM framework for defeasible entailment. We first present a class of basic defeasible entailment relations, characterise it in three distinct ways and provide a high-level algorithm for computing it. This framework is then refined, with the refined version being characterised in a similar manner. We show that the two well-known forms of defeasible entailment, rational closure and lexicographic closure, fall within our refined framework, that rational closure is the most conservative of the defeasible entailment relations within the framework (with respect to subset inclusion), but that there are forms of defeasible entailment within our framework that are more “adventurous” than lexicographic closure.},
  year = {2019},
  journal = {European Conference on Logics in Artificial Intelligence},
  pages = {182 - 197},
  month = {07/05 - 11/05},
  publisher = {Springer},
  address = {Switzerland},
  isbn = {978-3-030-19569-4},
  url = {https://link.springer.com/chapter/10.1007%2F978-3-030-19570-0_12},
  doi = {https://doi.org/10.1007/978-3-030-19570-0 _ 12},
}
Botha L, Meyer T, Peñaloza R. A Bayesian Extension of the Description Logic ALC. In: European Conference on Logics in Artificial Intelligence. Switzerland: Springer; 2019. doi:https://doi.org/10.1007/978-3-030-19570-0 _ 22.

Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. A probabilistic extension of a light-weight DL was recently proposed for dealing with certain knowledge occurring in uncertain contexts. In this paper, we continue that line of research by introducing the Bayesian extension BALC of the DL ALC. We present a tableau based procedure for deciding consistency, and adapt it to solve other probabilistic, contextual, and general inferences in this logic. We also show that all these problems remain ExpTime-complete, the same as reasoning in the underlying classical ALC.

@{237,
  author = {Leonard Botha and Thomas Meyer and Rafael Peñaloza},
  title = {A Bayesian Extension of the Description Logic ALC},
  abstract = {Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. A probabilistic extension of a light-weight DL was recently proposed for dealing with certain knowledge occurring in uncertain contexts. In this paper, we continue that line of research by introducing the Bayesian extension BALC of the DL ALC. We present a tableau based procedure for deciding consistency, and adapt it to solve other probabilistic, contextual, and general inferences in this logic. We also show that all these problems remain ExpTime-complete, the same as reasoning in the underlying classical ALC.},
  year = {2019},
  journal = {European Conference on Logics in Artificial Intelligence},
  pages = {339 - 354},
  month = {07/05 - 11/05},
  publisher = {Springer},
  address = {Switzerland},
  isbn = {978-3-030-19569-4},
  url = {https://link.springer.com/chapter/10.1007%2F978-3-030-19570-0_22},
  doi = {https://doi.org/10.1007/978-3-030-19570-0 _ 22},
}
Casini G, Meyer T, Varzinczak I. Simple Conditionals with Constrained Right Weakening. In: International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence; 2019. doi:10.24963/ijcai.2019/226.

In this paper we introduce and investigate a very basic semantics for conditionals that can be used to define a broad class of conditional reasoning systems. We show that it encompasses the most popular kinds of conditional reasoning developed in logic-based KR. It turns out that the semantics we propose is appropriate for a structural analysis of those conditionals that do not satisfy the property of Right Weakening. We show that it can be used for the further development of an analysis of the notion of relevance in conditional reasoning.

@{226,
  author = {Giovanni Casini and Thomas Meyer and Ivan Varzinczak},
  title = {Simple Conditionals with Constrained Right Weakening},
  abstract = {In this paper we introduce and investigate a very basic semantics for conditionals that can be used to define a broad class of conditional reasoning systems. We show that it encompasses the most popular kinds of conditional reasoning developed in logic-based KR. It turns out that the semantics we propose is appropriate for a structural analysis of those conditionals that do not satisfy the property of Right Weakening. We show that it can be used for the further development of an analysis of the notion of relevance in conditional reasoning.},
  year = {2019},
  journal = {International Joint Conference on Artificial Intelligence},
  pages = {1632-1638},
  month = {10/08-16/08},
  publisher = {International Joint Conferences on Artificial Intelligence},
  isbn = {978-0-9992411-4-1},
  url = {https://www.ijcai.org/Proceedings/2019/0226.pdf},
  doi = {10.24963/ijcai.2019/226},
}
Morris M, Ross T, Meyer T. Defeasible disjunctive datalog. In: Forum for Artificial Intelligence Research. CEUR; 2019. http://ceur-ws.org/Vol-2540/FAIR2019_paper_38.pdf.

Datalog is a declarative logic programming language that uses classical logical reasoning as its basic form of reasoning. Defeasible reasoning is a form of non-classical reasoning that is able to deal with exceptions to general assertions in a formal manner. The KLM approach to defeasible reasoning is an axiomatic approach based on the concept of plausible inference. Since Datalog uses classical reasoning, it is currently not able to handle defeasible implications and exceptions. We aim to extend the expressivity of Datalog by incorporating KLM-style defeasible reasoning into classical Datalog. We present a systematic approach to extending the KLM properties and a well-known form of defeasible entailment: Rational Closure. We conclude by exploring Datalog extensions of less conservative forms of defeasible entailment: Relevant and Lexicographic Closure.

@{225,
  author = {Matthew Morris and Tala Ross and Thomas Meyer},
  title = {Defeasible disjunctive datalog},
  abstract = {Datalog is a declarative logic programming language that uses classical logical reasoning as its basic form of reasoning. Defeasible reasoning is a form of non-classical reasoning that is able to deal with exceptions to general assertions in a formal manner. The KLM approach to defeasible reasoning is an axiomatic approach based on the concept of plausible inference. Since Datalog uses classical reasoning, it is currently not able to handle defeasible implications and exceptions. We aim to extend the expressivity of Datalog by incorporating KLM-style defeasible reasoning into classical Datalog. We present a systematic approach to extending the KLM properties and a well-known form of defeasible entailment: Rational Closure. We conclude by exploring Datalog extensions of less conservative forms of defeasible entailment: Relevant and Lexicographic Closure.},
  year = {2019},
  journal = {Forum for Artificial Intelligence Research},
  pages = {208-219},
  month = {03/12-06/12},
  publisher = {CEUR},
  isbn = {1613-0073},
  url = {http://ceur-ws.org/Vol-2540/FAIR2019_paper_38.pdf},
}
Harrison M, Meyer T. Rational preferential reasoning for datalog. In: Forum for Artificial Intelligence Research. CEUR; 2019. http://ceur-ws.org/Vol-2540/FAIR2019_paper_67.pdf.

Datalog is a powerful language that can be used to represent explicit knowledge and compute inferences in knowledge bases. Datalog cannot represent or reason about contradictory rules, though. This is a limitation as contradictions are often present in domains that contain exceptions. In this paper, we extend datalog to represent contradictory and defeasible information. We define an approach to efficiently reason about contradictory information in datalog and show that it satisfies the KLM requirements for a rational consequence relation. Finally, we introduce an implementation of this approach in the form of a defeasible datalog reasoning tool and evaluate the performance of this tool.

@{224,
  author = {Michael Harrison and Thomas Meyer},
  title = {Rational preferential reasoning for datalog},
  abstract = {Datalog is a powerful language that can be used to represent explicit knowledge and compute inferences in knowledge bases. Datalog cannot represent or reason about contradictory rules, though. This is a limitation as contradictions are often present in domains that contain exceptions. In this paper, we extend datalog to represent contradictory and defeasible information. We define an approach to efficiently reason
about contradictory information in datalog and show that it satisfies the KLM requirements for a rational consequence relation. Finally, we introduce an implementation of this approach in the form of a defeasible datalog reasoning tool and evaluate the performance of this tool.},
  year = {2019},
  journal = {Forum for Artificial Intelligence Research},
  pages = {232-243},
  month = {03/12-06/12},
  publisher = {CEUR},
  isbn = {1613-0073},
  url = {http://ceur-ws.org/Vol-2540/FAIR2019_paper_67.pdf},
}
Chingoma J, Meyer T. Forrester’s paradox using typicality. In: Forum for Artificial Intelligence Research. CEUR; 2019. http://ceur-ws.org/Vol-2540/FAIR2019_paper_54.pdf.

Deontic logic is a logic often used to formalise scenarios in the legal domain. Within the legal domain there are many exceptions and conflicting obligations. This motivates the enrichment of deontic logic with a notion of typicality which is based on defeasibility, with defeasibility allowing for reasoning about exceptions. Propositional Typicality Logic (PTL) is a logic that employs typicality. Deontic paradoxes are often used to examine logic systems as they provide undesirable results even if the scenarios seem intuitive. Forrester’s paradox is one of the most famous of these paradoxes. This paper shows that PTL can be used to represent and reason with Forrester’s paradox in such a way as to block undesirable conclusions without sacrificing desirable deontic properties.

@{223,
  author = {Julian Chingoma and Thomas Meyer},
  title = {Forrester’s paradox using typicality},
  abstract = {Deontic logic is a logic often used to formalise scenarios in the legal domain. Within the legal domain there are many exceptions and conflicting obligations. This motivates the enrichment of deontic logic with a notion of typicality which is based on defeasibility, with defeasibility allowing for reasoning about exceptions. Propositional Typicality Logic (PTL) is a logic that employs typicality. Deontic paradoxes are often used to examine logic systems as they provide undesirable results even if the scenarios seem intuitive. Forrester’s paradox is one of the most famous of these paradoxes. This paper shows that PTL can be used to represent and reason with Forrester’s paradox in such a way as to block undesirable conclusions without sacrificing desirable deontic properties.},
  year = {2019},
  journal = {Forum for Artificial Intelligence Research},
  pages = {220-231},
  month = {03/12-06/12},
  publisher = {CEUR},
  isbn = {1613-0073},
  url = {http://ceur-ws.org/Vol-2540/FAIR2019_paper_54.pdf},
}
Casini G, Harrison M, Meyer T, Swan R. Arbitrary Ranking of Defeasible Subsumption. 32nd International Work- shop on Description Logics. 2019. http://ceur-ws.org/Vol-2373/paper-9.pdf.

In this paper we propose an algorithm that generalises existing procedures for the implementation of defeasible reasoning in the framework of Description Logics (DLs). One of the well-known approaches to defeasible reasoning, the so-called KLM approach, is based on con- structing specific rankings of defeasible information, and using these rankings to determine priorities in case of conflicting information. Here we propose a procedure that allows us to input any possible ranking of the defeasible concept inclusions contained in the knowledge base. We analyse and investigate the forms of defeasible reasoning obtained when conclusions drawn are obtained using these rankings.

@misc{222,
  author = {Giovanni Casini and Michael Harrison and Thomas Meyer and Reid Swan},
  title = {Arbitrary Ranking of Defeasible Subsumption},
  abstract = {In this paper we propose an algorithm that generalises existing procedures for the implementation of defeasible reasoning in the framework of Description Logics (DLs). One of the well-known approaches to defeasible reasoning, the so-called KLM approach, is based on con- structing specific rankings of defeasible information, and using these rankings to determine priorities in case of conflicting information. Here we propose a procedure that allows us to input any possible ranking of the defeasible concept inclusions contained in the knowledge base. We analyse and investigate the forms of defeasible reasoning obtained when conclusions drawn are obtained using these rankings.},
  year = {2019},
  journal = {32nd International Work- shop on Description Logics},
  month = {06/2019},
  url = {http://ceur-ws.org/Vol-2373/paper-9.pdf},
}
Casini G, Straccia U, Meyer T. A polynomial Time Subsumption Algorithm for Nominal Safe ELO⊥ under Rational Closure. Information Sciences. 2019;501. doi:https://doi.org/10.1016/j.ins.2018.09.037.

Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe ELO⊥, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe ELO⊥ under RC that relies entirely on a series of classical, monotonic EL⊥ subsumption tests. Therefore, any existing classical monotonic EL⊥ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability.

@article{221,
  author = {Giovanni Casini and Umberto Straccia and Thomas Meyer},
  title = {A polynomial Time Subsumption Algorithm for Nominal Safe ELO⊥ under Rational Closure},
  abstract = {Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe ELO⊥, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe ELO⊥ under RC that relies entirely on a series of classical, monotonic EL⊥ subsumption tests. Therefore, any existing classical monotonic EL⊥ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability.},
  year = {2019},
  journal = {Information Sciences},
  volume = {501},
  pages = {588 - 620},
  publisher = {Elsevier},
  isbn = {0020-0255},
  url = {http://www.sciencedirect.com/science/article/pii/S0020025518307436},
  doi = {https://doi.org/10.1016/j.ins.2018.09.037},
}
Leenen L, Meyer T. Artificial Intelligence and Big Data Analytics in Support of Cyber Defense. In: Developments in Information Security and Cybernetic Wars. United States of America: Information Science Reference, IGI Global; 2019. doi:10.4018/978-1-5225-8304-2.ch002.

Cybersecurity analysts rely on vast volumes of security event data to predict, identify, characterize, and deal with security threats. These analysts must understand and make sense of these huge datasets in order to discover patterns which lead to intelligent decision making and advance warnings of possible threats, and this ability requires automation. Big data analytics and artificial intelligence can improve cyber defense. Big data analytics methods are applied to large data sets that contain different data types. The purpose is to detect patterns, correlations, trends, and other useful information. Artificial intelligence provides algorithms that can reason or learn and improve their behavior, and includes semantic technologies. A large number of automated systems are currently based on syntactic rules which are generally not sophisticated enough to deal with the level of complexity in this domain. An overview of artificial intelligence and big data technologies in cyber defense is provided, and important areas for future research are identified and discussed.

@inbook{220,
  author = {Louise Leenen and Thomas Meyer},
  title = {Artificial Intelligence and Big Data Analytics in Support of Cyber Defense},
  abstract = {Cybersecurity analysts rely on vast volumes of security event data to predict, identify, characterize, and deal with security threats. These analysts must understand and make sense of these huge datasets in order to discover patterns which lead to intelligent decision making and advance warnings of possible threats, and this ability requires automation. Big data analytics and artificial intelligence can improve cyber defense. Big data analytics methods are applied to large data sets that contain different data types. The purpose is to detect patterns, correlations, trends, and other useful information. Artificial intelligence provides algorithms that can reason or learn and improve their behavior, and includes semantic technologies. A large number of automated systems are currently based on syntactic rules which are generally not sophisticated enough to deal with the level of complexity in this domain. An overview of artificial intelligence and big data technologies in cyber defense is provided, and important areas for future research are identified and discussed.},
  year = {2019},
  journal = {Developments in Information Security and Cybernetic Wars},
  pages = {42 - 63},
  publisher = {Information Science Reference, IGI Global},
  address = {United States of America},
  isbn = {9781522583042},
  doi = {10.4018/978-1-5225-8304-2.ch002},
}
Booth R, Casini G, Meyer T, Varzinczak I. On rational entailment for Propositional Typicality Logic. Artificial Intelligence . 2019;227. doi:https://doi.org/10.1016/j.artint.2019.103178.

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence holds. The semantics of PTL is in terms of ranked models as studied in the well-known KLM approach to preferential reasoning and therefore KLM-style rational consequence relations can be embedded in PTL. In spite of the non-monotonic features introduced by the semantics adopted for the typicality operator, the obvious Tarskian definition of entailment for PTL remains monotonic and is therefore not appropriate in many contexts. Our first important result is an impossibility theorem showing that a set of proposed postulates that at first all seem appropriate for a notion of entailment with regard to typicality cannot be satisfied simultaneously. Closer inspection reveals that this result is best interpreted as an argument for advocating the development of more than one type of PTL entailment. In the spirit of this interpretation, we investigate three different (semantic) versions of entailment for PTL, each one based on the definition of rational closure as introduced by Lehmann and Magidor for KLM-style conditionals, and constructed using different notions of minimality.

@article{219,
  author = {Richard Booth and Giovanni Casini and Thomas Meyer and Ivan Varzinczak},
  title = {On rational entailment for Propositional Typicality Logic},
  abstract = {Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence holds. The semantics of PTL is in terms of ranked models as studied in the well-known KLM approach to preferential reasoning and therefore KLM-style rational consequence relations can be embedded in PTL. In spite of the non-monotonic features introduced by the semantics adopted for the typicality operator, the obvious Tarskian definition of entailment for PTL remains monotonic and is therefore not appropriate in many contexts. Our first important result is an impossibility theorem showing that a set of proposed postulates that at first all seem appropriate for a notion of entailment with regard to typicality cannot be satisfied simultaneously. Closer inspection reveals that this result is best interpreted as an argument for advocating the development of more than one type of PTL entailment. In the spirit of this interpretation, we investigate three different (semantic) versions of entailment for PTL, each one based on the definition of rational closure as introduced by Lehmann and Magidor for KLM-style conditionals, and constructed using different notions of minimality.},
  year = {2019},
  journal = {Artificial Intelligence},
  volume = {227},
  pages = {103178},
  publisher = {Elsevier},
  isbn = {0004-3702},
  url = {https://www.sciencedirect.com/science/article/abs/pii/S000437021830506X?via%3Dihub},
  doi = {https://doi.org/10.1016/j.artint.2019.103178},
}

2018

Meyer T, Leenen L. Semantic Technologies and Big Data Analytics for Cyber Defence. In: Information Retrieval and Management: Concepts, Methodologies, Tools, and Applications. IGI Global; 2018. https://researchspace.csir.co.za/dspace/bitstream/handle/10204/8932/Leenen_2016.pdf?sequence=1.

The Governments, military forces and other organisations responsible for cybersecurity deal with vast amounts of data that has to be understood in order to lead to intelligent decision making. Due to the vast amounts of information pertinent to cybersecurity, automation is required for processing and decision making, specifically to present advance warning of possible threats. The ability to detect patterns in vast data sets, and being able to understanding the significance of detected patterns are essential in the cyber defence domain. Big data technologies supported by semantic technologies can improve cybersecurity, and thus cyber defence by providing support for the processing and understanding of the huge amounts of information in the cyber environment. The term big data analytics refers to advanced analytic techniques such as machine learning, predictive analysis, and other intelligent processing techniques applied to large data sets that contain different data types. The purpose is to detect patterns, correlations, trends and other useful information. Semantic technologies is a knowledge representation paradigm where the meaning of data is encoded separately from the data itself. The use of semantic technologies such as logicbased systems to support decision making is becoming increasingly popular. However, most automated systems are currently based on syntactic rules. These rules are generally not sophisticated enough to deal with the complexity of decisions required to be made. The incorporation of semantic information allows for increased understanding and sophistication in cyber defence systems. This paper argues that both big data analytics and semantic technologies are necessary to provide counter measures against cyber threats. An overview of the use of semantic technologies and big data technologies in cyber defence is provided, and important areas for future research in the combined domains are discussed.

@inbook{206,
  author = {Thomas Meyer and Louise Leenen},
  title = {Semantic Technologies and Big Data Analytics for Cyber Defence},
  abstract = {The Governments, military forces and other organisations responsible for cybersecurity deal with vast amounts of data that has to be understood in order to lead to intelligent decision making. Due to the vast amounts of information pertinent to cybersecurity, automation is required for processing and decision making, specifically to present advance warning of possible threats. The ability to detect patterns in vast data sets, and being able to understanding the significance of detected patterns are essential in the cyber defence domain. Big data technologies supported by semantic technologies can improve cybersecurity, and thus cyber defence by providing support for the processing and understanding of the huge amounts of information in the cyber environment.
The term big data analytics refers to advanced analytic techniques such as machine learning, predictive analysis, and other intelligent processing techniques applied to large data sets that contain different data types. The purpose is to detect patterns, correlations, trends and other useful information. Semantic technologies is a knowledge representation paradigm where the meaning of data is encoded separately from the data itself. The use of semantic technologies such as logicbased systems to support decision making is becoming increasingly popular. However, most automated systems are currently based on syntactic rules. These rules are generally not sophisticated enough to deal with the complexity of decisions required to be made. The incorporation of semantic information allows for increased understanding and sophistication in cyber defence systems.
This paper argues that both big data analytics and semantic technologies are necessary to provide counter measures against cyber threats. An overview of the use of semantic technologies and big data technologies in cyber defence is provided, and important areas for future research in the combined domains are discussed.},
  year = {2018},
  journal = {Information Retrieval and Management: Concepts, Methodologies, Tools, and Applications},
  pages = {1375-1388},
  publisher = {IGI Global},
  isbn = {9781522551911},
  url = {https://researchspace.csir.co.za/dspace/bitstream/handle/10204/8932/Leenen_2016.pdf?sequence=1},
}
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