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A Polynomial Time Subsumption Algorithm for Nominal Safe $ELO_{\bot}$ under Rational Closure Casini, Giovanni ; ; in Information Sciences (in press) 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 ... [more ▼] 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 $ELO_{\bot}$, 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 $ELO_{\bot}$ under RC that relies entirely on a series of classical, monotonic $EL_{\bot}$ subsumption tests. Therefore, any existing classical monotonic $EL_{\bot}$ 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. [less ▲] Detailed reference viewed: 78 (13 UL)On Rational Entailment for Propositional Typicality Logic ; Casini, Giovanni ; et al in Artificial Intelligence (in press) Propositional Typicality Logic (PTL) is a recently proposed logic, ob- tained by enriching classical propositional logic with a typicality opera- tor capturing the most typical (alias normal or ... [more ▼] Propositional Typicality Logic (PTL) is a recently proposed logic, ob- tained by enriching classical propositional logic with a typicality opera- tor 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 preferen- tial 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 impossibil- ity 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 in- vestigate 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. [less ▲] Detailed reference viewed: 27 (0 UL)Taking Defeasible Entailment beyond Rational Closure Casini, Giovanni ; ; in Proceedings of the 16th European Conference on Logics in Artificial Intelligence (JELIA-19) (2019) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 65 (6 UL)Arbitrary Ranking of Defeasible Subsumption Casini, Giovanni ; ; et al in Proceedings of the 32nd International Workshop on Description Logics (2019) 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 ... [more ▼] 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 constructing 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. [less ▲] Detailed reference viewed: 44 (3 UL)A KLM Perspective on Defeasible Reasoning for Description Logics ; Casini, Giovanni ; et al in Turhan, Anni-Yasmin; Wolter, Frank; Lutz, Carsten (Eds.) et al Description Logic, Theory Combination, and All That - Essays Dedicated to Franz Baader on the Occasion of His 60th Birthday (2019) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 49 (3 UL)Simple Conditionals with Constrained Right Weakening Casini, Giovanni ; ; in Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI 2019) (2019) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 52 (5 UL)A Semantic Perspective on Belief Change in a Preferential Non-Monotonic Framework Casini, Giovanni ; ; et al in Proceedings of the Sixteenth International Conference on Principles of Knowledge Representation and Reasoning (KR 2018) (2018) Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we investigate the ... [more ▼] Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we investigate the integration of the two formalisms by studying belief change for a (preferential) non-monotonic framework. We show that the standard AGM approach to be- lief change can be transferred to a preferential non-monotonic framework in the sense that change operations can be defined on conditional knowledge bases. We take as a point of depar- ture the results presented by Casini and Meyer (2017), and we develop and extend such results with characterisations based on semantics and entrenchment relations, showing how some of the constructions defined for propositional logic can be lifted to our preferential non-monotonic framework. [less ▲] Detailed reference viewed: 85 (24 UL)Defeasible Entailment: from Rational Closure to Lexicographic Closure and Beyond Casini, Giovanni ; ; in Proceeding of the 17th International Workshop on Non-Monotonic Reasoning (NMR 2018) (2018) In this paper we present what we believe to be the first systematic approach for extending the framework for de- feasible entailment first presented by Kraus, Lehmann, and Magidor—the so-called KLM ... [more ▼] In this paper we present what we believe to be the first systematic approach for extending the framework for de- feasible entailment first presented by Kraus, Lehmann, and Magidor—the so-called KLM approach. Drawing on the properties for KLM, we first propose a class of basic defea- sible entailment relations. We characterise this basic frame- work in three ways: (i) semantically, (ii) in terms of a class of properties, and (iii) in terms of ranks on statements in a knowlege base. We also provide an algorithm for computing the basic framework. These results are proved through vari- ous representation results. We then refine this framework by defining the class of rational defeasible entailment relations. This refined framework is also characterised in thee ways: se- mantically, in terms of a class of properties, and in terms of ranks on statements. We also provide an algorithm for com- puting the refined framework. Again, these results are proved through various representation results. We argue that the class of rational defeasible entail- ment relations—a strengthening of basic defeasible entail- ment which is itself a strengthening of the original KLM proposal—is worthy of the term rational in the sense that all of them can be viewed as appropriate forms of defeasi- ble entailment. We show that the two well-known forms of defeasible entailment, rational closure and lexicographic clo- sure, fall within our rational defeasible framework. We show that rational closure is the most conservative of the defeasi- ble entailment relations within the framework (with respect to subset inclusion), but that there are forms of defeasible en- tailment within our framework that are more “adventurous” than lexicographic closure. [less ▲] Detailed reference viewed: 77 (9 UL)On Rational Entailment for Propositional Typicality Logic Casini, Giovanni ; ; et al Report (2018) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 59 (0 UL)Legal Knowledge and Information Systems - JURIX 2017: The Thirtieth Annual Conference ; Casini, Giovanni Book published by IOS Press BV (2017) The proceedings of the 30th International Conference on Legal Knowledge and Information Systems – JURIX 2017. For three decades, the JURIX conferences have been held under the auspices of the Dutch ... [more ▼] The proceedings of the 30th International Conference on Legal Knowledge and Information Systems – JURIX 2017. For three decades, the JURIX conferences have been held under the auspices of the Dutch Foundation for Legal Knowledge Based Systems (www.jurix.nl). In the time, it has become a European conference in terms of the diverse venues throughout Europe and the nationalities of participants. [less ▲] Detailed reference viewed: 144 (4 UL)Belief Change in a Preferential Non-Monotonic Framework Casini, Giovanni ; in Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence (2017, August) Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we show that we can ... [more ▼] Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we show that we can also integrate the two formalisms by studying belief change within a (preferential) non-monotonic framework. This integration relies heavily on the identification of the monotonic core of a non-monotonic framework. We consider belief change operators in a non-monotonic propositional setting with a view towards preserving consistency. These results can also be applied to the preservation of coherence—an important notion within the field of logic-based ontologies. We show that the standard AGM approach to belief change can be adapted to a preferential non-monotonic framework, with the definition of expansion, contraction, and revision operators, and corresponding representation results. Surprisingly, preferential AGM belief change, as defined here, can be obtained in terms of classical AGM belief change. [less ▲] Detailed reference viewed: 196 (5 UL)Postulates for Revocation Schemes Cramer, Marcos ; Casini, Giovanni in Cramer, Marcos; Casini, Giovanni (Eds.) Principles of Security and Trust. Proceedings of the 6th International Conference POST 2017 (2017, January 18) In access control frameworks with the possibility of delegating permissions and administrative rights, delegation chains can form. There are di erent ways to treat these delegation chains when revoking ... [more ▼] In access control frameworks with the possibility of delegating permissions and administrative rights, delegation chains can form. There are di erent ways to treat these delegation chains when revoking rights, which give rise to di erent revocation schemes. Hagstr om et al. [11] proposed a framework for classifying revocation schemes, in which the di erent revocation schemes are de ned graph-theoretically. At the outset, we identify multiple problems with Hagstr om et al.'s de nitions of the revocation schemes, which can pose security risks. This paper is centered around the question how one can systematically ensure that improved de nitions of the revocation schemes do not lead to similar problems. For this we propose to apply the axiomatic method originating in social choice theory to revocation schemes. Our use of the axiomatic method resembles its use in belief revision theory. This means that we de ne postulates that describe the desirable behaviour of revocation schemes, study which existing revocation frameworks satisfy which postulates, and show how all de ned postulates can be satis ed by de ning the revocation schemes in a novel way. [less ▲] Detailed reference viewed: 171 (39 UL)Extending Typicality for Description Logics ; Casini, Giovanni ; et al Report (2017) Recent extensions of description logics for dealing with different forms of non-monotonic reasoning don’t take us beyond the case of defeasible subsumption. In this paper we enrich the DL EL⊥ with a ... [more ▼] Recent extensions of description logics for dealing with different forms of non-monotonic reasoning don’t take us beyond the case of defeasible subsumption. In this paper we enrich the DL EL⊥ with a (constrained version of) a typicality operator •, the intuition of which is to capture the most typical members of a class, providing us with the DL EL•⊥. We argue that EL•⊥ is the smallest step one can take to increase the expressivity beyond the case of defeasible subsumption for DLs, while still retaining all the rationality properties an appropriate notion of defeasible subsumption is required to satisfy, and investigate what an appropriate notion of non-monotonic entailment for EL•⊥ should look like. [less ▲] Detailed reference viewed: 70 (4 UL)DARe-17 - Proceedings of the Fourth International Workshop on Defeasible and Ampliative Reasoning ; Casini, Giovanni ; Book published by CEUR Workshop Proceedings (2017) Proceedings of the 4th International Workshop on Defeasible and Ampliative Reasoning (DARe-17), co-located with the 14th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR-17 ... [more ▼] Proceedings of the 4th International Workshop on Defeasible and Ampliative Reasoning (DARe-17), co-located with the 14th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR-17). Espoo, Finland, July 3—6, 2017. [less ▲] Detailed reference viewed: 66 (2 UL)Using Defeasible Information to Obtain Coherence Casini, Giovanni ; in Baral, Chitta; Delgrande, James; Wolter, Frank (Eds.) Proceedings of the 15th International Conference on Principle of Knowledge Representation and Reasoning (KR-16) (2016, April) We consider the problem of obtaining coherence in a propositional knowledge base using techniques from Belief Change. Our motivation comes from the field of formal ontologies where coherence is ... [more ▼] We consider the problem of obtaining coherence in a propositional knowledge base using techniques from Belief Change. Our motivation comes from the field of formal ontologies where coherence is interpreted to mean that a concept name has to be satisfiable. In the propositional case we consider here, this translates to a propositional formula being satisfiable. We define belief change operators in a framework of nonmonotonic preferential reasoning.We show how the introduction of defeasible information using contraction operators can be an effective means for obtaining coherence. [less ▲] Detailed reference viewed: 51 (16 UL)Revising Incompletely Specified Convex Probabilistic Belief Bases ; ; Casini, Giovanni in Kern-Isberner,, Gabriele; Wassermann, Renata (Eds.) Proceedings of the 16th International Workshop on Non-Monotonic Reasoning (NMR 2016) (2016, April) We propose a method for an agent to revise its incomplete probabilistic beliefs when a new piece of propositional information is observed. In this work, an agent’s beliefs are represented by a set of ... [more ▼] We propose a method for an agent to revise its incomplete probabilistic beliefs when a new piece of propositional information is observed. In this work, an agent’s beliefs are represented by a set of probabilistic formulae – a belief base. The method involves determining a representative set of ‘boundary’ probability distributions consistent with the current belief base, revising each of these probability distributions and then translating the revised information into a new belief base. We use a version of Lewis Imaging as the revision operation. The correctness of the approach is proved. The expressivity of the belief bases under consideration are rather restricted, but has some applications. We also discuss methods of belief base revision employing the notion of optimum entropy, and point out some of the benefits and difficulties in those methods. Both the boundary distribution method and the optimum entropy method are reasonable, yet yield different results. [less ▲] Detailed reference viewed: 35 (3 UL)Using Defeasible Information to Obtain Coherence Casini, Giovanni ; in BNAIC 2016 - Proceedings of the 28th Benelux Conference on Artificial intelligence (2016) In this paper we consider the problem of obtaining coherence in a propositional knowledge base using techniques from Belief Change. Our motivation comes from the field of formal ontologies where coherence ... [more ▼] In this paper we consider the problem of obtaining coherence in a propositional knowledge base using techniques from Belief Change. Our motivation comes from the field of formal ontologies where coherence is interpreted to mean that a concept name has to be satisfiable. [less ▲] Detailed reference viewed: 29 (4 UL)DARe-16 - Proceedings of the International Workshop on Defeasible and Ampliative Reasoning ; Casini, Giovanni ; et al Book published by CEUR Workshop Proceedings (2016) Proceedings of the International Workshop on Defeasible and Ampliative Reasoning (DARe-16), co-located with the 22th European Conference on Artificial Intelligence (ECAI 2016). The Hague, Holland, August ... [more ▼] Proceedings of the International Workshop on Defeasible and Ampliative Reasoning (DARe-16), co-located with the 22th European Conference on Artificial Intelligence (ECAI 2016). The Hague, Holland, August 29, 2016. [less ▲] Detailed reference viewed: 43 (4 UL)On Revision of Partially Specified Convex Probabilistic Belief Bases ; ; Casini, Giovanni in Proceedings of the 22nd European Conference on Artificial Intelligence (ECAI-16) (2016) We propose a method for an agent to revise its incomplete probabilistic beliefs when a new piece of propositional information is observed. In this work, an agent’s beliefs are represented by a set of ... [more ▼] We propose a method for an agent to revise its incomplete probabilistic beliefs when a new piece of propositional information is observed. In this work, an agent’s beliefs are represented by a set of probabilistic formulae – a belief base. The method involves determining a representative set of ‘boundary’ probability distributions consistent with the current belief base, revising each of these probability distributions and then translating the revised information into a new belief base. We use a version of Lewis Imaging as the revision operation. The correctness of the approach is proved. An analysis of the approach is done against six rationality postulates. The expressivity of the belief bases under consideration are rather restricted, but has some applications. We also discuss methods of belief base revision employing the notion of optimum entropy, and point out some of the benefits and difficulties in those methods. Both the boundary distribution method and the optimum entropy methods are reasonable, yet yield different results. [less ▲] Detailed reference viewed: 84 (6 UL)A non-classical logical foundation for naturalised realism ; Casini, Giovanni ; in Arazim, Pavel; Dančák, michal (Eds.) The Logica Yearbook (2015) Detailed reference viewed: 75 (4 UL) |
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