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2022 Conference article Open Access OPEN

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

See at: link.springer.com Open Access | ISTI Repository Open Access | CNR ExploRA Open Access


2022 Report Open Access OPEN

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 via OpenAIRE

See at: arxiv.org Open Access | ISTI Repository Open Access | CNR ExploRA Open Access


2022 Report Open Access OPEN

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 via OpenAIRE

See at: arxiv.org Open Access | ISTI Repository Open Access | CNR ExploRA Open Access


2021 Conference article Open Access OPEN

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

See at: ojs.aaai.org Open Access | ISTI Repository Open Access | CNR ExploRA Open Access


2021 Report Open Access OPEN

Situated conditional reasoning
Casini G., Meyer T., Varzinczak I.
Conditionals are useful for modelling, but aren't always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive than classical conditionals, are general enough to be used in several application domains, and are able to distinguish, for example, between expectations and counterfactuals. Formally, they are shown to generalise the conditional setting in the style of Kraus, Lehmann, and Magidor. We show that situation-based conditionals can be described in terms of a set of rationality postulates. We then propose an intuitive semantics for these conditionals, and present a representation result which shows that our semantic construction corresponds exactly to the description in terms of postulates. With the semantics in place, we proceed to define a form of entailment for situated conditional knowledge bases, which we refer to as minimal closure. It is reminiscent of and, indeed, inspired by, the version of entailment for propositional conditional knowledge bases known as rational closure. Finally, we proceed to show that it is possible to reduce the computation of minimal closure to a series of propositional entailment and satisfiability checks. While this is also the case for rational closure, it is somewhat surprising that the result carries over to minimal closure.Source: ISTI Technical Report, ISTI-2021-TR/009, 2021
DOI: 10.32079/isti-tr-2021/009

See at: ISTI Repository Open Access | CNR ExploRA Open Access


2021 Conference article Open Access OPEN

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

See at: drive.google.com Open Access | ISTI Repository Open Access | CNR ExploRA Open Access


2021 Report Open Access OPEN

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

See at: ISTI Repository Open Access | CNR ExploRA Open Access


2021 Contribution to journal Open Access OPEN

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

See at: collegepublications.co.uk Open Access | CNR ExploRA Open Access


2021 Report Open Access OPEN

InfraScience Research Activity Report 2020
Artini M., Assante M., Atzori C., Baglioni M., Bardi A., Candela L., Casini G., Castelli D., Cirillo R., Coro G., Debole F., Dell'Amico A., Frosini L., La Bruzzo S., Lazzeri E., Lelii L., Manghi P., Mangiacrapa F., Mannocci A., Pagano P., Panichi G., Piccioli T., Sinibaldi F., Straccia U.
InfraScience is a research group of the National Research Council of Italy - Institute of Information Science and Technologies (CNR - ISTI) based in Pisa, Italy. This report documents the research activity performed by this group in 2020 to highlight the major results. In particular, the InfraScience group confronted with research challenges characterising Data Infrastructures, e\-Sci\-ence, and Intelligent Systems. The group activity is pursued by closely connecting research and development and by promoting and supporting open science. In fact, the group is leading the development of two large scale infrastructures for Open Science, \ie D4Science and OpenAIRE. During 2020 InfraScience members contributed to the publishing of 30 papers, to the research and development activities of 12 research projects (11 funded by EU), to the organization of conferences and training events, to several working groups and task forces.Source: ISTI Annual Report, ISTI-2021-AR/002, pp.1–20, 2021
DOI: 10.32079/isti-ar-2021/002
Project(s): ARIADNEplus via OpenAIRE, Blue Cloud via OpenAIRE, PerformFISH via OpenAIRE, EOSC-Pillar via OpenAIRE, DESIRA via OpenAIRE, EOSCsecretariat.eu via OpenAIRE, RISIS 2 via OpenAIRE, TAILOR via OpenAIRE, I-GENE via OpenAIRE, MOVING via OpenAIRE, OpenAIRE-Advance via OpenAIRE, SoBigData-PlusPlus via OpenAIRE

See at: ISTI Repository Open Access | CNR ExploRA Open Access


2020 Report Open Access OPEN

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

See at: ISTI Repository Open Access | CNR ExploRA Open Access


2020 Contribution to conference Open Access OPEN

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

See at: ceur-ws.org Open Access | ISTI Repository Open Access | CNR ExploRA Open Access


2020 Conference article Open Access OPEN

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

See at: nmr2020.dc.uba.ar Open Access | ISTI Repository Open Access | CNR ExploRA Open Access


2020 Conference article Open Access OPEN

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

See at: library.confdna.com Open Access | ISTI Repository Open Access | CNR ExploRA Open Access | academic.microsoft.com Restricted | dblp.uni-trier.de Restricted | proceedings.kr.org Restricted | proceedings.kr.org Restricted


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

See at: ACM Transactions on Computational Logic Restricted | UM Publications Restricted | ACM Transactions on Computational Logic Restricted | dl.acm.org Restricted | ACM Transactions on Computational Logic Restricted | CNR ExploRA Restricted | ACM Transactions on Computational Logic Restricted


2020 Conference article Open Access OPEN

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 via OpenAIRE

See at: ISTI Repository Open Access | OpenAIRE Restricted | link.springer.com Restricted | CNR ExploRA Restricted


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

See at: academic.microsoft.com Restricted | dblp.uni-trier.de Restricted | link.springer.com Restricted | link.springer.com Restricted | CNR ExploRA Restricted | www.umbertostraccia.it Restricted