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2020
Contribution to conference
Open Access
Proceedings of the 4th International Workshop on MIning and REasoning with Legal texts (MIREL 2019)
Casini G., Di Caro L., Governatori G., Leone V., Markovich R.
Proceedings of the 4th International Workshop on MIning and REasoning with Legal texts (MIREL 2019), co-located with the 32nd International Conference on Legal Knowledge and Information Systems (JURIX 2019).Source: Aachen: CEUR-WS.org, 2020
Casini G., Di Caro L., Governatori G., Leone V., Markovich R.
Proceedings of the 4th International Workshop on MIning and REasoning with Legal texts (MIREL 2019), co-located with the 32nd International Conference on Legal Knowledge and Information Systems (JURIX 2019).Source: Aachen: CEUR-WS.org, 2020
See at:
ceur-ws.org 
| ISTI Repository | CNR ExploRA
2020
Conference article
Open Access
BKLM - An expressive logic for defeasible reasoning
Paterson-Jones G., Casini G., Meyer T.
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.Source: 18th INTERNATIONAL WORKSHOP ON NON-MONOTONIC REASONING (NMR 2020), pp. 170–178, online conference, due to COVID-19 pandemic, 12-14/09/2020
Paterson-Jones G., Casini G., Meyer T.
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.Source: 18th INTERNATIONAL WORKSHOP ON NON-MONOTONIC REASONING (NMR 2020), pp. 170–178, online conference, due to COVID-19 pandemic, 12-14/09/2020
See at:
nmr2020.dc.uba.ar | ISTI Repository | CNR ExploRA
2020
Conference article
Open Access
Rational defeasible belief change
Casini G., Meyer T., Varzinczak I.
We present a formal framework for modelling belief change within a nonmonotonic 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 consideration of the problem of iterated change, generalising the classical work of Darwiche and Pearl. We characterise a family of operators for iterated revision, followed by an analogous characterisation of operators for iterated contraction. We start considering belief change operators aimed at preserving logical consistency, and then characterise analogous operators aimed at the preservation of coherence--an important notion within the field of logic-based ontologies.Source: 17th International Conference on Principles of Knowledge Representation and Reasoning (KR2020), pp. 213–222, Online conference, 12-18/09/2020
DOI: 10.24963/kr.2020/22
Metrics:
Casini G., Meyer T., Varzinczak I.
We present a formal framework for modelling belief change within a nonmonotonic 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 consideration of the problem of iterated change, generalising the classical work of Darwiche and Pearl. We characterise a family of operators for iterated revision, followed by an analogous characterisation of operators for iterated contraction. We start considering belief change operators aimed at preserving logical consistency, and then characterise analogous operators aimed at the preservation of coherence--an important notion within the field of logic-based ontologies.Source: 17th International Conference on Principles of Knowledge Representation and Reasoning (KR2020), pp. 213–222, Online conference, 12-18/09/2020
DOI: 10.24963/kr.2020/22
Metrics:
See at:
library.confdna.com | ISTI Repository | doi.org 
| www.scopus.com | CNR ExploRA
2020
Journal article
Restricted
Principles of KLM-style Defeasible Description Logics
Britz K., Casini G., Meyer T., Moodley K., Sattler U., Varzinczak I.
The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for both preferential and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level of entailment and present an algorithm for the computation of rational closure of a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DL ALC.Source: ACM transactions on computational logic 22 (2020): 1–46. doi:10.1145/3420258
DOI: 10.1145/3420258
Metrics:
Britz K., Casini G., Meyer T., Moodley K., Sattler U., Varzinczak I.
The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for both preferential and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level of entailment and present an algorithm for the computation of rational closure of a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DL ALC.Source: ACM transactions on computational logic 22 (2020): 1–46. doi:10.1145/3420258
DOI: 10.1145/3420258
Metrics:
See at:
NARCIS | dl.acm.org | ACM Transactions on Computational Logic | CNR ExploRA
2021
Conference article
Open Access
Contextual conditional reasoning
Casini G., Meyer T., Varzinczak I.
We extend the expressivity of classical conditional reasoning by introducing context as a new parameter. The enriched conditional logic generalises the defeasible conditional setting in the style of Kraus, Lehmann, and Magidor, and allows for a refined semantics that is able to distinguish, for example, between expectations and counterfactuals. In this paper we introduce the language for the enriched logic and define an appropriate semantic framework for it. We analyse which properties generally associated with conditional reasoning are still satisfied by the new semantic framework, provide a suitable representation result, and define an entailment relation based on Lehmann and Magidor's generally-accepted notion of Rational Closure.Source: AAAI-21 - The Thirty-Fifth AAAI Conference on Artificial Intelligence, pp. 6254–6261, Online Conference, 2-9/2/2021
Casini G., Meyer T., Varzinczak I.
We extend the expressivity of classical conditional reasoning by introducing context as a new parameter. The enriched conditional logic generalises the defeasible conditional setting in the style of Kraus, Lehmann, and Magidor, and allows for a refined semantics that is able to distinguish, for example, between expectations and counterfactuals. In this paper we introduce the language for the enriched logic and define an appropriate semantic framework for it. We analyse which properties generally associated with conditional reasoning are still satisfied by the new semantic framework, provide a suitable representation result, and define an entailment relation based on Lehmann and Magidor's generally-accepted notion of Rational Closure.Source: AAAI-21 - The Thirty-Fifth AAAI Conference on Artificial Intelligence, pp. 6254–6261, Online Conference, 2-9/2/2021
See at:
ojs.aaai.org | ISTI Repository | CNR ExploRA
2021
Contribution to journal
Open Access
Guest editorial Special Issue: Mining and Reasoning with Legal Texts
Robaldo L, Van Der Torre L., Casini G., Villata S.
Journal of Applied Logics - IfCoLog Journal, vol. 8 (4). Special Issue: Mining and Reasoning with Legal TextsSource: London: College Publications Ltd, 2021
Robaldo L, Van Der Torre L., Casini G., Villata S.
Journal of Applied Logics - IfCoLog Journal, vol. 8 (4). Special Issue: Mining and Reasoning with Legal TextsSource: London: College Publications Ltd, 2021
See at:
collegepublications.co.uk | ISTI Repository | CNR ExploRA
2020
Conference article
Open Access
A boolean extension of KLM-Style conditional reasoning
Paterson-Jones G., Casini G., Meyer T.
Propositional KLM-style defeasible reasoning involves extending propositional logic with a new logical connective that can express defeasible (or conditional) implications, with semantics given by ordered 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 BKLMis 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 dierent forms of PTL entailment proposed by Booth et al. to apply to BKLM.Source: SACAIR 2020 - First Southern African Conference for AI Research, pp. 236–252, Muldersdrift, South Africa, February 22-26, 2021
DOI: 10.1007/978-3-030-66151-9_15
Project(s): TAILOR
Metrics:
Paterson-Jones G., Casini G., Meyer T.
Propositional KLM-style defeasible reasoning involves extending propositional logic with a new logical connective that can express defeasible (or conditional) implications, with semantics given by ordered 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 BKLMis 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 dierent forms of PTL entailment proposed by Booth et al. to apply to BKLM.Source: SACAIR 2020 - First Southern African Conference for AI Research, pp. 236–252, Muldersdrift, South Africa, February 22-26, 2021
DOI: 10.1007/978-3-030-66151-9_15
Project(s): TAILOR
Metrics:
See at:
ISTI Repository | OpenAIRE | link.springer.com | CNR ExploRA
2022
Contribution to conference
Open Access
Proceedings of the 20th International Workshop on Non-Monotonic Reasoning (NMR 2022)
Arieli O., Casini G., Giordano L.
Proceedings of the 20th International Workshop on Non-Monotonic Reasoning (NMR2022)
Arieli O., Casini G., Giordano L.
Proceedings of the 20th International Workshop on Non-Monotonic Reasoning (NMR2022)
See at:
ceur-ws.org | ISTI Repository | CNR ExploRA
2022
Contribution to book
Open Access
Handbook of legal AI
Casini G., Robaldo L., Van Der Torre L., Villata S.
The Handbook of Legal AI presents a comprehensive overview of the state-of-the-art and trends in the research field of legal AI. The handbook provides a solid introduction to the essentials of the field for newcomers and a selection of advanced issues as a base for future research directions. As the law gets more complex, conflicting, and ever-changing, more advanced methods, most of them come from the Artifi cial Intelligence (AI) field, are required for analyzing, representing and reasoning on legal knowledge. The discipline that tackles these challenges is now known as "Legal Artificial Intelligence". Legal AI is experiencing, in particular, in the latest years growth in activity, also at the industrial level, touching a variety of issues which go from the analysis of the textual content of the law, to reasoning about legal interpretation to ethical issues of AI applications in the legal domain (e.g., the artificial judge). This Handbook presents a collection of chapters which evolves around three main topics, namely norm mining (i.e., how to automatically identify, extract, classify and interlink norms from text), reasoning about norms and regulations (i.e., how to derive new legal knowledge from the existing legal knowledge bases in such a way to address automatic legal decision making), and norm enforcement and compliance (i.e., how to check and ensure the compliance of the systems' requirements with the regulation).Source: London: College Publications Ltd, 2022
Project(s): TAILOR
Casini G., Robaldo L., Van Der Torre L., Villata S.
The Handbook of Legal AI presents a comprehensive overview of the state-of-the-art and trends in the research field of legal AI. The handbook provides a solid introduction to the essentials of the field for newcomers and a selection of advanced issues as a base for future research directions. As the law gets more complex, conflicting, and ever-changing, more advanced methods, most of them come from the Artifi cial Intelligence (AI) field, are required for analyzing, representing and reasoning on legal knowledge. The discipline that tackles these challenges is now known as "Legal Artificial Intelligence". Legal AI is experiencing, in particular, in the latest years growth in activity, also at the industrial level, touching a variety of issues which go from the analysis of the textual content of the law, to reasoning about legal interpretation to ethical issues of AI applications in the legal domain (e.g., the artificial judge). This Handbook presents a collection of chapters which evolves around three main topics, namely norm mining (i.e., how to automatically identify, extract, classify and interlink norms from text), reasoning about norms and regulations (i.e., how to derive new legal knowledge from the existing legal knowledge bases in such a way to address automatic legal decision making), and norm enforcement and compliance (i.e., how to check and ensure the compliance of the systems' requirements with the regulation).Source: London: College Publications Ltd, 2022
Project(s): TAILOR
See at:
www.collegepublications.co.uk | CNR ExploRA
2022
Journal article
Open Access
Normative change: an AGM approach
Maranhão J. S. A., Casini G., Van Der Torre L., Pigozzi G.
Studying normative change has practical and theoretical interests. Changing legal rules poses interpretation problems to determine the content of legal rules. The question of interpretation is tightly linked to those of determining the validity and the ability to produce effects of legal rules. Different formal models of normative change seem better suited to capture these dimensions: the dimension of validity appears to be better captured by the AGM approach, whereas syntactic methods are better suited to model how rules' effects are blocked or enabled. Historically, the AGM approach of belief revision (on which we focus in this chapter) was the first formal model of normative change. We provide a survey on the AGM approach along with the main criticisms made to it. We then turn to a formal analysis of normative change that combines AGM theory and input/output logic, allowing for a clear distinction between norms and obligations. Our approach addresses some of the difficulties of normative change, like the combination of constitutive and regulative rules (and the normative conflicts that may arise from such a combination), the revision and contraction of normative systems, as well as the contraction of normative systems that combine sets of constitutive and regulative rules. We end our chapter by highlighting and discussing some challenges and open problems of normative change in the AGM approach.Source: IfCoLog Journal of Logics and their Applications 9 (2022): 825–889.
Project(s): TAILOR
Maranhão J. S. A., Casini G., Van Der Torre L., Pigozzi G.
Studying normative change has practical and theoretical interests. Changing legal rules poses interpretation problems to determine the content of legal rules. The question of interpretation is tightly linked to those of determining the validity and the ability to produce effects of legal rules. Different formal models of normative change seem better suited to capture these dimensions: the dimension of validity appears to be better captured by the AGM approach, whereas syntactic methods are better suited to model how rules' effects are blocked or enabled. Historically, the AGM approach of belief revision (on which we focus in this chapter) was the first formal model of normative change. We provide a survey on the AGM approach along with the main criticisms made to it. We then turn to a formal analysis of normative change that combines AGM theory and input/output logic, allowing for a clear distinction between norms and obligations. Our approach addresses some of the difficulties of normative change, like the combination of constitutive and regulative rules (and the normative conflicts that may arise from such a combination), the revision and contraction of normative systems, as well as the contraction of normative systems that combine sets of constitutive and regulative rules. We end our chapter by highlighting and discussing some challenges and open problems of normative change in the AGM approach.Source: IfCoLog Journal of Logics and their Applications 9 (2022): 825–889.
Project(s): TAILOR
See at:
www.collegepublications.co.uk | CNR ExploRA
2010
Conference article
Restricted
Rational closure for defeasible description logics
Casini G., Straccia U.
In the field of non-monotonic logics, the notion of rational closure is acknowledged as a landmark, and we are going to see that such a construction can be characterised by means of a simple method in the context of propositional logic. We then propose an application of our approach to rational closure in the field of Description Logics, an important knowledge representation formalism, and provide a simple decision procedure for this case.Source: 12th European Conference on Logics in Artificial Intelligence (JELIA-10), pp. 77–90, Helsinki, Finland, 13-15 September 2010
DOI: 10.1007/978-3-642-15675-5_9
Metrics:
Casini G., Straccia U.
In the field of non-monotonic logics, the notion of rational closure is acknowledged as a landmark, and we are going to see that such a construction can be characterised by means of a simple method in the context of propositional logic. We then propose an application of our approach to rational closure in the field of Description Logics, an important knowledge representation formalism, and provide a simple decision procedure for this case.Source: 12th European Conference on Logics in Artificial Intelligence (JELIA-10), pp. 77–90, Helsinki, Finland, 13-15 September 2010
DOI: 10.1007/978-3-642-15675-5_9
Metrics:
See at:
doi.org | link.springer.com | CNR ExploRA
2020
Report
Open Access
Defeasible RDFS via rational closure
Casini G., Straccia U.
In the field of non-monotonic logics, the notion of Rational Closure (RC) is acknowledged as a prominent approach. In recent years, RC has gained even more popularity in the context of Description Logics (DLs), the logic underpinning the semantic web standard ontology language OWL 2, whose main ingredients are classes and roles. In this work, we show how to integrate RC within the triple language RDFS, which together with OWL2 are the two major standard semantic web ontology languages. To do so, we start from ?df, which is the logic behind RDFS, and then extend it to ?df?, allowing to state that two entities are incompatible. Eventually, we propose defeasible ?df? via a typical RC construction. The main features of our approach are: (i) unlike most other approaches that add an extra non-monotone rule layer on top of monotone RDFS, defeasible ?df? remains syntactically a triple language and is a simple extension of ?df? by introducing some new predicate symbols with specific semantics. In particular, any RDFS reasoner/store may handle them as ordinary terms if it does not want to take account for the extra semantics of the new predicate symbols; (ii) the defeasible ?df? entailment decision procedure is build on top of the ?df? entailment decision procedure, which in turn is an extension of the one for ?df via some additional inference rules favouring an potential implementation; and (iii) defeasible ?df? entailment can be decided in polynomial time.Source: ISTI Technical Reports 008/2020, 2020
DOI: 10.32079/isti-tr-2020/008
Metrics:
Casini G., Straccia U.
In the field of non-monotonic logics, the notion of Rational Closure (RC) is acknowledged as a prominent approach. In recent years, RC has gained even more popularity in the context of Description Logics (DLs), the logic underpinning the semantic web standard ontology language OWL 2, whose main ingredients are classes and roles. In this work, we show how to integrate RC within the triple language RDFS, which together with OWL2 are the two major standard semantic web ontology languages. To do so, we start from ?df, which is the logic behind RDFS, and then extend it to ?df?, allowing to state that two entities are incompatible. Eventually, we propose defeasible ?df? via a typical RC construction. The main features of our approach are: (i) unlike most other approaches that add an extra non-monotone rule layer on top of monotone RDFS, defeasible ?df? remains syntactically a triple language and is a simple extension of ?df? by introducing some new predicate symbols with specific semantics. In particular, any RDFS reasoner/store may handle them as ordinary terms if it does not want to take account for the extra semantics of the new predicate symbols; (ii) the defeasible ?df? entailment decision procedure is build on top of the ?df? entailment decision procedure, which in turn is an extension of the one for ?df via some additional inference rules favouring an potential implementation; and (iii) defeasible ?df? entailment can be decided in polynomial time.Source: ISTI Technical Reports 008/2020, 2020
DOI: 10.32079/isti-tr-2020/008
Metrics:
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ISTI Repository | CNR ExploRA
2021
Conference article
Open Access
KLM-style defeasibility for restricted first-order logic
Casini G., Meyer T., Paterson-Jones G.
We extend the KLM approach to defeasible reasoning to be applicable to a restricted version of first-order logic. We describe defeasibility for this logic using a set of rationality postulates, provide an appropriate semantics for it, and present a representation result that characterises the semantic description of defeasibility in terms of the rationality postulates. Based on this theoretical core, we then propose a version of defeasible entailment that is inspired by Rational Closure as it is defined for defeasible propositional logic and defeasible description logics. We show that this form of defeasible entailment is rational in the sense that it adheres to our rationality postulates. The work in this paper is the first step towards our ultimate goal of introducing KLM-style defeasible reasoning into the family of Datalog+/- ontology languages.Source: NMR 2021 - 19th International Workshop on Non-Monotonic Reasoning, pp. 184–193, Online Conference, 3-5/11/2021
Casini G., Meyer T., Paterson-Jones G.
We extend the KLM approach to defeasible reasoning to be applicable to a restricted version of first-order logic. We describe defeasibility for this logic using a set of rationality postulates, provide an appropriate semantics for it, and present a representation result that characterises the semantic description of defeasibility in terms of the rationality postulates. Based on this theoretical core, we then propose a version of defeasible entailment that is inspired by Rational Closure as it is defined for defeasible propositional logic and defeasible description logics. We show that this form of defeasible entailment is rational in the sense that it adheres to our rationality postulates. The work in this paper is the first step towards our ultimate goal of introducing KLM-style defeasible reasoning into the family of Datalog+/- ontology languages.Source: NMR 2021 - 19th International Workshop on Non-Monotonic Reasoning, pp. 184–193, Online Conference, 3-5/11/2021
See at:
drive.google.com | ISTI Repository | CNR ExploRA
2022
Conference article
Open Access
A rational entailment for expressive description logics via description logic programs
Casini G., Straccia U.
Lehmann and Magidor's rational closure is acknowledged as a land-mark in the field of non-monotonic logics and it has also been re-formulated in the context ofDescription Logics (DLs). We show here how to model a rational form of entailment for expressive DLs, such as SROIQ, providing a novel reasoning procedure that compiles a non-monotone DL knowledge base into a description logic program(dl-program).Source: SACAIR 2021 - Second Southern African Conference, pp. 177–191, Durban, South Africa, 6-10/12/2021
DOI: 10.1007/978-3-030-95070-5_12
Metrics:
Casini G., Straccia U.
Lehmann and Magidor's rational closure is acknowledged as a land-mark in the field of non-monotonic logics and it has also been re-formulated in the context ofDescription Logics (DLs). We show here how to model a rational form of entailment for expressive DLs, such as SROIQ, providing a novel reasoning procedure that compiles a non-monotone DL knowledge base into a description logic program(dl-program).Source: SACAIR 2021 - Second Southern African Conference, pp. 177–191, Durban, South Africa, 6-10/12/2021
DOI: 10.1007/978-3-030-95070-5_12
Metrics:
See at:
ISTI Repository | link.springer.com | CNR ExploRA
2021
Report
Open Access
A rational entailment for expressive description logics via description logic programs
Casini G., Straccia U.
Lehmann and Magidor's rational closure is acknowledged as a landmark in the field of non-monotonic logics and it has also been re-formulated in the context of Description Logics (DLs). We show here how to model a rational form of entailment for expressive DLs, such as SROIQ, providing a novel reasoning procedure that compiles a nonmonotone DL knowledge base into a description logic program (dl-program).Source: ISTI Technical Report, ISTI-2021-TR/019, 2021
DOI: 10.32079/isti-tr-2021/019
Metrics:
Casini G., Straccia U.
Lehmann and Magidor's rational closure is acknowledged as a landmark in the field of non-monotonic logics and it has also been re-formulated in the context of Description Logics (DLs). We show here how to model a rational form of entailment for expressive DLs, such as SROIQ, providing a novel reasoning procedure that compiles a nonmonotone DL knowledge base into a description logic program (dl-program).Source: ISTI Technical Report, ISTI-2021-TR/019, 2021
DOI: 10.32079/isti-tr-2021/019
Metrics:
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ISTI Repository | CNR ExploRA
2022
Report
Open Access
A general framework for modelling conditional reasoning - Preliminary report
Casini G., Straccia U.
We introduce and investigate here a formalisation for conditionals that allows the definition of a broad class of reasoning systems. This framework covers the most popular kinds of conditional reasoning in logic-based KR: the semantics we propose is appropriate for a structural analysis of those conditionals that do not satisfy closure properties associated to classical logics.Source: ISTI Technical Report, ISTI-2022-TR/004, pp.1–21, 2022
Project(s): TAILOR
Casini G., Straccia U.
We introduce and investigate here a formalisation for conditionals that allows the definition of a broad class of reasoning systems. This framework covers the most popular kinds of conditional reasoning in logic-based KR: the semantics we propose is appropriate for a structural analysis of those conditionals that do not satisfy closure properties associated to classical logics.Source: ISTI Technical Report, ISTI-2022-TR/004, pp.1–21, 2022
Project(s): TAILOR
See at:
arxiv.org | ISTI Repository | CNR ExploRA
2022
Report
Open Access
A minimal deductive system for RDFS with negative statements
Straccia U., Casini G.
The triple language RDFS is designed to represent and reason with \emph{positive} statements only (e.g."antipyretics are drugs"). In this paper we show how to extend RDFS to express and reason with various forms of negative statements under the Open World Assumption (OWA). To do so, we start from rdf, a minimal, but significant RDFS fragment that covers all essential features of RDFS, and then extend it to ?rdfbotneg, allowing express also statements such as "radio therapies are non drug treatments", "Ebola has no treatment", or "opioids and antipyretics are disjoint classes". The main and, to the best of our knowledge, unique features of our proposal are: (i) rdfbotneg remains syntactically a triple language by extending rdf with new symbols with specific semantics and there is no need to revert to the reification method to represent negative triples; (ii) the logic is defined in such a way that any RDFS reasoner/store may handle the new predicates as ordinary terms if it does not want to take account of the extra capabilities; (iii) despite negated statements, every rdfbotneg knowledge base is satisfiable; (iv) the rdfbotneg entailment decision procedure is obtained from rdf via additional inference rules favouring a potential implementation; and (v) deciding entailment in rdfbotneg ranges from P to NP.Source: ISTI Technical Report, ISTI-2022-TR/005, pp.1–24, 2022
Project(s): TAILOR
Straccia U., Casini G.
The triple language RDFS is designed to represent and reason with \emph{positive} statements only (e.g."antipyretics are drugs"). In this paper we show how to extend RDFS to express and reason with various forms of negative statements under the Open World Assumption (OWA). To do so, we start from rdf, a minimal, but significant RDFS fragment that covers all essential features of RDFS, and then extend it to ?rdfbotneg, allowing express also statements such as "radio therapies are non drug treatments", "Ebola has no treatment", or "opioids and antipyretics are disjoint classes". The main and, to the best of our knowledge, unique features of our proposal are: (i) rdfbotneg remains syntactically a triple language by extending rdf with new symbols with specific semantics and there is no need to revert to the reification method to represent negative triples; (ii) the logic is defined in such a way that any RDFS reasoner/store may handle the new predicates as ordinary terms if it does not want to take account of the extra capabilities; (iii) despite negated statements, every rdfbotneg knowledge base is satisfiable; (iv) the rdfbotneg entailment decision procedure is obtained from rdf via additional inference rules favouring a potential implementation; and (v) deciding entailment in rdfbotneg ranges from P to NP.Source: ISTI Technical Report, ISTI-2022-TR/005, pp.1–24, 2022
Project(s): TAILOR
See at:
arxiv.org | ISTI Repository | CNR ExploRA
2022
Conference article
Open Access
A general framework for modelling conditional reasoning - Preliminary report
Casini G., Straccia U.
We introduce and investigate here a formalisation for conditionals that allows the definition of a broad class of reasoning systems. This framework covers the most popular kinds of conditional reasoning in logic-based KR: the semantics we propose is appropriate for a structural analysis of those conditionals that do not satisfy closure properties associated to classical logics.Source: KR 2022 - 19th International Conference on Principles of Knowledge Representation and Reasoning, pp. 112–121, Haifa, Israel, 31/07-05/08/2022
DOI: 10.24963/kr.2022/12
DOI: 10.48550/arxiv.2202.07596
Project(s): TAILOR
Metrics:
Casini G., Straccia U.
We introduce and investigate here a formalisation for conditionals that allows the definition of a broad class of reasoning systems. This framework covers the most popular kinds of conditional reasoning in logic-based KR: the semantics we propose is appropriate for a structural analysis of those conditionals that do not satisfy closure properties associated to classical logics.Source: KR 2022 - 19th International Conference on Principles of Knowledge Representation and Reasoning, pp. 112–121, Haifa, Israel, 31/07-05/08/2022
DOI: 10.24963/kr.2022/12
DOI: 10.48550/arxiv.2202.07596
Project(s): TAILOR
Metrics:
See at:
arXiv.org e-Print Archive | ISTI Repository | proceedings.kr.org | doi.org | doi.org | CNR ExploRA
2022
Conference article
Open Access
A minimal deductive system for RDFS with negative statements
Straccia U., Casini G.
The triple language RDFS is designed to represent and reason with \emph{positive} statements only (e.g."antipyretics are drugs"). In this paper we show how to extend RDFS to express and reason with various forms of negative statements under the Open World Assumption (OWA). To do so, we start from rdf, a minimal, but significant RDFS fragment that covers all essential features of RDFS, and then extend it to ?rdfbotneg, allowing express also statements such as "radio therapies are non drug treatments", "Ebola has no treatment", or "opioids and antipyretics are disjoint classes". The main and, to the best of our knowledge, unique features of our proposal are: (i) rdfbotneg remains syntactically a triple language by extending rdf with new symbols with specific semantics and there is no need to revert to the reification method to represent negative triples; (ii) the logic is defined in such a way that any RDFS reasoner/store may handle the new predicates as ordinary terms if it does not want to take account of the extra capabilities; (iii) despite negated statements, every rdfbotneg knowledge base is satisfiable; (iv) the rdfbotneg entailment decision procedure is obtained from rdf via additional inference rules favouring a potential implementation; and (v) deciding entailment in rdfbotneg ranges from P to NP.Source: KR 2022 - 19th International Conference on Principles of Knowledge Representation and Reasoning, pp. 351–361, Haifa, Israel, 31/07-05/08/2022
DOI: 10.24963/kr.2022/35
DOI: 10.48550/arxiv.2202.13750
Project(s): TAILOR
Metrics:
Straccia U., Casini G.
The triple language RDFS is designed to represent and reason with \emph{positive} statements only (e.g."antipyretics are drugs"). In this paper we show how to extend RDFS to express and reason with various forms of negative statements under the Open World Assumption (OWA). To do so, we start from rdf, a minimal, but significant RDFS fragment that covers all essential features of RDFS, and then extend it to ?rdfbotneg, allowing express also statements such as "radio therapies are non drug treatments", "Ebola has no treatment", or "opioids and antipyretics are disjoint classes". The main and, to the best of our knowledge, unique features of our proposal are: (i) rdfbotneg remains syntactically a triple language by extending rdf with new symbols with specific semantics and there is no need to revert to the reification method to represent negative triples; (ii) the logic is defined in such a way that any RDFS reasoner/store may handle the new predicates as ordinary terms if it does not want to take account of the extra capabilities; (iii) despite negated statements, every rdfbotneg knowledge base is satisfiable; (iv) the rdfbotneg entailment decision procedure is obtained from rdf via additional inference rules favouring a potential implementation; and (v) deciding entailment in rdfbotneg ranges from P to NP.Source: KR 2022 - 19th International Conference on Principles of Knowledge Representation and Reasoning, pp. 351–361, Haifa, Israel, 31/07-05/08/2022
DOI: 10.24963/kr.2022/35
DOI: 10.48550/arxiv.2202.13750
Project(s): TAILOR
Metrics:
See at:
arXiv.org e-Print Archive | ISTI Repository | proceedings.kr.org | doi.org | doi.org | CNR ExploRA
2022
Conference article
Open Access
Defeasible reasoning in RDFS
Casini G., Straccia U.
For non-monotonic logics, the notion of Rational Closure (RC) is acknowledged as one of the main approaches. In this work we present an integration of RC within the triple language RDFS (Resource Description Framework Schema), which together with OWL 2 is a major standard semantic web ontology language. To do so, we start from ?df, an RDFS fragment that covers the essential features of RDFS, and extend it to ?df?, allowing to state that two entities are incompatible/disjoint with each other. Eventually, we propose defeasible ?df? via a typical RC construction allowing to state default class/property inclusions.Source: NMR 2022 - International Workshop on Non-Monotonic Reasoning 2022, pp. 155–158, Haifa, Israel, 07-09/08/2022
Project(s): TAILOR
Casini G., Straccia U.
For non-monotonic logics, the notion of Rational Closure (RC) is acknowledged as one of the main approaches. In this work we present an integration of RC within the triple language RDFS (Resource Description Framework Schema), which together with OWL 2 is a major standard semantic web ontology language. To do so, we start from ?df, an RDFS fragment that covers the essential features of RDFS, and extend it to ?df?, allowing to state that two entities are incompatible/disjoint with each other. Eventually, we propose defeasible ?df? via a typical RC construction allowing to state default class/property inclusions.Source: NMR 2022 - International Workshop on Non-Monotonic Reasoning 2022, pp. 155–158, Haifa, Israel, 07-09/08/2022
Project(s): TAILOR
See at:
ceur-ws.org | ISTI Repository | CNR ExploRA