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We address the problem of compiling defeasible theories to Datalog¬ programs. We prove the correctness of this compilation, for the defeasible logic DL(∂||), but the techniques we use apply to many other defeasible logics. Structural properties of DL(∂||) are identified that support efficient implementation and/or approximation of the conclusions of defeasible theories in the logic, compared with other defeasible logics. We also use previously well-studied structural properties of logic programs to adapt to incomplete Datalog¬ implementations.

Reasoning on defeasible knowledge is a topic of interest in the area of description logics, as it is related to the need of representing exceptional instances in knowledge bases. In this direction, in our previous works we presented a framework for representing (contextualized) OWL RL knowledge bases with a notion of justified exceptions on defeasible axioms: reasoning in such framework is realized by a translation into ASP programs. The resulting reasoning process for OWL RL, however, introduces a complex encoding in order to capture reasoning on the negative information needed for reasoning on exceptions. In this paper, we apply the justified exception approach to knowledge bases in , that is, the language underlying OWL QL. We provide a definition for knowledge bases with defeasible axioms and study their semantic and computational properties. In particular, we study the effects of exceptions over unnamed individuals. The limited form of axioms allows us to formulate a simpler ASP encoding, where reasoning on negative information is managed by direct rules. The resulting materialization method gives rise to a complete reasoning procedure for instance checking in with defeasible axioms.1

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 .

Devising adaptive logics usually starts with a set of abnormalities and a deductive logic. Where the adaptive logic is ampliative, the deductive logic is the lower limit logic, the rules of which are unconditionally valid. Where the adaptive logic is corrective, the deductive logic is the upper limit logic, the rules of which are valid in case the premises do not require any abnormalities to be true. In some cases, the idea for devising an adaptive logic does not relate to a set of abnormalities, but to one or more defeasible rules, and perhaps also to one of the deductive logics. Defeasible rules are not universally valid, but are valid in ‘normal situations’ or for unproblematic parts of premise set. Where the idea is such, the set of abnormalities has to be delineated in view of the rules. The way in which this task may be tackled is by no means obvious and is the main topic studied in the present paper. The outcome is an extremely simple and transparent recipe. It is shown that, except for very special cases, the recipe leads to an adequate result.

Assumption-based argumentation is one of the most prominent formalisms for logical (or structured) argumentation, with tight links to different forms of defeasible reasoning. In this paper we study the Dung semantics for extended forms of assumption-based argumentation frameworks (ABFs), based on any contrapositive propositional logic, and whose defeasible assumptions are expressed by arbitrary formulas in that logic. We show that unless the falsity propositional constant is part of the defeasible assumptions, the grounded and the well-founded semantics for ABFs lack most of the desirable properties they have in abstract argumentation frameworks (AAFs), and that for simple definitions of the contrariness operator and the attacks relations, preferred and stable semantics are reduced to naive semantics. We also show the redundancy of the closure condition in the standard definition of Dung's semantics for ABFs, and investigate the use of disjunctive attacks in this setting. Finally, we show some close relations of reasoning with ABFs to reasoning with maximally consistent sets of premises, and consider some properties of the induced entailments, such as being cumulative, preferential, or rational relations that satisfy non-interference.

Η τεχνητή νοημοσύνη (AI), είναι ο κλάδος πληροφορικής που ασχολείται με τη σχεδίαση και την υλοποίηση ευφυών συστημάτων ικανά να συλλέγουν πληροφορίες, να εκτελούν ανάλυση δεδομένων και να εφαρμόζουν κατάλληλες ενέργειες, για να καλύψουν τις ανάγκες διαφόρων περιβαλλόντων, μιμούμενα την ανθρώπινη συμπεριφορά ως προς την συλλογιστική, μάθηση και επίλυση προβλημάτων. Τα κλινικά συστήματα υποστήριξης αποφάσεων είναι συστήματα τεχνητής νοημοσύνης που υποστηρίζουν τη διαδικασία λήψης αποφάσεων των ιατρών. Η παρούσα διατριβή επικεντρώνεται στην ανάπτυξη του κλινικού συστήματος υποστήριξης αποφάσεων CDS-RA για την διαχείριση και μακροπρόθεσμη πρόγνωση ασθενών με ρευματοειδή αρθρίτιδα υπό βιολογική θεραπεία. Ένας σημαντικός στόχος του CDS-RA συστήματος είναι να παρέχει προγνωστική λειτουργικότητα ικανή για την πρώιμη πρόβλεψη του επιπέδου επίμονης νόσου ενός ασθενούς με ρευματοειδή αρθρίτιδα υπό βιολογική θεραπεία. Το επίπεδο επίμονης νόσου ορίστηκε ως το ίδιο επίπεδο δραστηριότητας της νόσου, που παρουσιάστηκε σε έναν ασθενή υπό βιολογική θεραπεία, για τουλάχιστον το ήμισυ της 5ετούς κλινικής παρακολούθησης, σωρευτικά και ανεξάρτητα από τις διακυμάνσεις. Η διατριβή αναλύει τη σχέση των επιπέδων επίμονης χαμηλής (LDA), μέτριας (MDA) και υψηλής (HDA) νόσου με διαφορετικά μακροπρόθεσμα αποτελέσματα, όσο αφορά (α) την πενταετή πορεία λειτουργικότητας των ασθενών και (β) το σύνολο σοβαρών ανεπιθύμητων συμβάντων στα 5 χρόνια βιολογικής θεραπείας. Αναπτύχθηκε ένα πολυπαραγοντικό μοντέλο μεικτών επιδράσεων (mixed-effect model) με βάση τις πενταετές πορείες λειτουργικότητας των ασθενών που έδειξε ότι οι ασθενείς με MDA συσχετίστηκαν με χειρότερη πορεία λειτουργικότητας 5 ετών από τους ασθενείς με LDA ενώ οι ασθενείς με HDA συσχετίστηκαν με ακόμη υψηλότερο περιορισμό λειτουργικότητας 5 ετών από τους LDA ασθενείς. Οι ασθενείς με MDA υπο-κατηγοριοποιήθηκαν σε δύο υπο-ομάδες χαμηλότερης και υψηλότερης MDA. Ένα δεύτερο πολυπαραγοντικό μοντέλο μεικτών επιδράσεων έδειξε ότι η υπό-ομάδα σε υψηλότερη MDA συσχετίστηκε με χειρότερη πορεία λειτουργικότητας 5 ετών από την υπό-ομάδα σε χαμηλότερη MDA. Παρόμοια διαφοροποίηση παρουσίασαν τα σοβαρά ανεπιθύμητα συμβάντα. Επίσης, δύο πολυπαραγοντικά προβλεπτικά μοντέλα λογιστικής παλινδρόμησης (logistic regression) από το πεδίο της μηχανικής μάθησης αναπτύχθηκαν για την εξατομικευμένη πρόβλεψη του επιπέδου επίμονης νόσου ενός ασθενή από πρώιμα δεδομένα θεραπείας. Τα μοντέλα ανέδειξαν πρώιμους δείκτες για τα επιπέδα επίμονης χαμηλής, μέτριας και υψηλής νόσου. Το σύστημα CDS-RA περιλαμβάνει ακόμα λειτουργικότητα τεχνητής νοημοσύνης (AI) που υποστηρίζει την πρόγνωση του επιπέδου επίπονης νόσου ενός ασθενή υπό βιολογική θεραπεία, βασισμένη σε τρεις στοιχειοθετημένες πολιτικές που εκφράστηκαν με λογικούς κανόνες αναιρέσιμης συλλογιστικής. Συνολικά, το CDS-RA παρέχει ένα τεχνολογικό περιβάλλον τεχνητής νοημοσύνης με ευρύ φάσμα λειτουργικών υπηρεσιών που παρέχει εξατομικευμένες προγνωστικές πληροφορίες για την μακροπρόθεσμη έκβαση των ασθενών υπό βιολογική θεραπεία. Οι καινοτόμες υπηρεσίες του συστήματος χρησιμοποιούν πολυπαραγοντικά μοντέλα μεικτών επιδράσεων, προβλεπτικά μοντέλα μηχανικής μάθησης και αναιρέσιμη συλλογιστική, για να παρέχουν πολύτιμες προγνωστικές πληροφορίες κατά την διαδικασία κλινικών αποφάσεων. Το σύστημα CDS-RA στοχεύει στην υποστήριξη των κλινικών ιατρών κατα την βιολογική θεραπεία ασθενών με ρευματοειδή αρθρίτιδα ώστε να βελτιωθούν τα αποτελέσματα τους.

“Real knowledge,” as I use the term, is the most highly prized form of true belief sought by an epistemic agent. This paper argues that defeasible infinitism provides a good way to characterize real knowledge and it shows how real knowledge can arise from fallible justification. Then, I argue that there are two ways of interpreting Ernest Sosa's account of real knowledge as belief that is aptly formed and capable of being fully defended.On the one hand, if beliefs are aptly formed only if they have a specific causal etiology, namely that they are efficiently caused fully or partially by virtuous characteristics of the epistemic agent, then Sosa's account falls prey to what I call the problem of the Hazard of Empirical Disconfirmation (HED). The HED problem applies to all forms of causal accounts of real knowledge and is simply that as we gain more empirical knowledge about the causal origins of our true beliefs that are the most highly prized we will discover that they do not always (or even hardly ever) satisfy the required efficient causal constraints. Bluntly put, having sufficiently good reasons for our beliefs might not require that the beliefs have the requisite efficient causal etiology.On the other hand, there is a way of interpreting Sosa's views that does not include an efficient causal prerequisite. That interpretation makes Sosa's account of real knowledge almost identical to defeasible infinitism but expressed in an alternate vocabulary. Such a view is not subject to the HED problem and it can solve the deep problem in epistemology, namely how to get epistemically certain (as opposed to psychologically certain) knowledge from fallible justification.

Description logics have been extended in a number of ways to support defeasible reasoning in the KLM tradition. Such features include preferential or rational defeasible concept inclusion, and defeasible roles in complex concept descriptions. Semantically, defeasible subsumption is obtained by means of a preference order on objects, while defeasible roles are obtained by adding a preference order to role interpretations. In this paper, we address an important limitation in defeasible extensions of description logics, namely the restriction in the semantics of defeasible concept inclusion to a single preference order on objects. We do this by inducing a modular preference order on objects from each modular preference order on roles, and using these to relativise defeasible subsumption. This yields a notion of contextualised rational defeasible subsumption, with contexts described by roles. We also provide a semantic construction for rational closure and a method for its computation, and present a correspondence result between the two.

Efforts to formalize qualitative accounts of inference to the best explanation (IBE) confront two obstacles: the imprecise nature of such accounts and the unusual logical properties that explanatio...

The exact relationship between formal argumentation and nonmonotonic logics is a research topic that keeps on eluding researchers despite recent intensified efforts. We contribute to a deeper understanding of this relation by investigating characterizations of abstract dialectical frameworks in conditional logics for nonmonotonic reasoning. We first show that in general, there is a gap between argumentation and conditional semantics when applying several intuitive translations, but then prove that this gap can be closed when focusing on specific classes of translations., Annals of mathematics and artificial intelligence;Bd 89. 2021, H. 10/11, S. 1075-1099

IntroductionTransparency of computation is a requirement for assessing the validity of computed results and research claims based upon them; and it is essential for access to, assessment, and reuse of computational components. These components may be subject to methodological or other challenges over time. While reference to archived software and/or data is increasingly common in publications, a single machine-interpretable, integrative representation of how results were derived, that supports defeasible reasoning, has been absent.MethodsWe developed the Evidence Graph Ontology, EVI, in OWL 2, with a set of inference rules, to provide deep representations of supporting and challenging evidence for computations, services, software, data, and results, across arbitrarily deep networks of computations, in connected or fully distinct processes. EVI integrates FAIR practices on data and software, with important concepts from provenance models, and argumentation theory. It extends PROV for additional expressiveness, with support for defeasible reasoning. EVI treats any computational result or component of evidence as a defeasible assertion, supported by a DAG of the computations, software, data, and agents that produced it.ResultsWe have successfully deployed EVI for large-scale predictive analytics on clinical time-series data. Every result may reference its evidence graph as metadata, which can be extended when subsequent computations are executed.DiscussionEvidence graphs support transparency and defeasible reasoning on results. They are first-class computational objects and reference the datasets and software from which they are derived. They support fully transparent computation, with challenge and support propagation. The EVI approach may be extended to include instruments, animal models, and critical experimental reagents.

In this paper we introduce hypersequent-based frameworks for the modelling of defeasible reasoning by means of logic-based argumentation and the induced entailment relations. These structures are an extension of sequent-based argumentation frameworks, in which arguments and the attack relations among them are expressed not only by Gentzen-style sequents, but by more general expressions, called hypersequents. This generalization allows us to overcome some of the known weaknesses of logical argumentation frameworks and to prove several desirable properties of the entailments that are induced by the extended (hypersequent-based) frameworks. It also allows us to incorporate as the deductive base of our formalism some well-known logics (like the intermediate logic , the modal logic , and the relevance logic ), which lack cut-free sequent calculi, and so are not adequate for standard sequent-based argumentation. We show that hypersequent-based argumentation yields robust defeasible variants of these logics, with many desirable properties.

Knowledge-representation and reasoning methods have been extensively researched within Artificial Intelligence. Among these, argumentation has emerged as an ideal paradigm for inference under uncertainty with conflicting knowledge. Its value has been predominantly demonstrated via analyses of the topological structure of graphs of arguments and its formal properties. However, limited research exists on the examination and comparison of its inferential capacity in real-world modelling tasks and against other knowledge-representation and non-monotonic reasoning methods. This study is focused on a novel comparison between defeasible argumentation and non-monotonic fuzzy reasoning when applied to the representation of the ill-defined construct of human mental workload and its assessment. Different argument-based and non-monotonic fuzzy reasoning models have been designed considering knowledge-bases of incremental complexity containing uncertain and conflicting information provided by a human reasoner. Findings showed how their inferences have a moderate convergent and face validity when compared respectively to those of an existing baseline instrument for mental workload assessment, and to a perception of mental workload self-reported by human participants. This confirmed how these models also reasonably represent the construct under consideration. Furthermore, argument-based models had on average a lower mean squared error against the self-reported perception of mental workload when compared to fuzzy-reasoning models and the baseline instrument. The contribution of this research is to provide scholars, interested in formalisms on knowledge-representation and non-monotonic reasoning, with a novel approach for empirically comparing their inferential capacity.

In this paper we investigate the relationships between a multipreferential semantics for defeasible reasoning in knowledge representation and a deep neural network model. Weighted knowledge bases for description logics are considered under a “concept-wise” multipreference semantics. The semantics is further extended to fuzzy interpretations and exploited to provide a preferential interpretation of Multilayer Perceptrons, under some condition.

Defeasible reasoning is the mode of reasoning where conclusions can be overturned by taking into account new evidence. A commonly used method in cognitive science and logic literature is to handcraft argumentation supporting inference graphs. While humans find inference graphs very useful for reasoning, constructing them at scale is difficult. In this paper, we automatically generate such inference graphs through transfer learning from another NLP task that shares the kind of reasoning that inference graphs support. Through automated metrics and human evaluation, we find that our method generates meaningful graphs for the defeasible inference task. Human accuracy on this task improves by 20% by consulting the generated graphs. Our findings open up exciting new research avenues for cases where machine reasoning can help human reasoning. (A dataset of 230,000 influence graphs for each defeasible query is located at: https://tinyurl.com/defeasiblegraphs.), Findings of the Association for Computational Linguistics: ACL 2021

This paper presents a contextual defeasible reasoning based multi-agent formalism to model heterogeneous systems using the notion of a multi-context system. This framework relies on the semantic knowledge sources which allow us to model context-aware non-monotonic reasoning agents to infer the desired goals using the extracted rules from the ontologies and handles inconsistencies using conflicting contextual information. We illustrate the validity and correctness of the proposed formalism using a simple case study of a smart healthcare system with the prototypal implementation of the system.

Introduction: Transparency of computation is a requirement for assessing the validity of computed results and research claims based upon them; and it is essential for access to, assessment, and reuse of computational components. These components may be subject to methodological or other challenges over time. While reference to archived software and/or data is increasingly common in publications, a single machine-interpretable, integrative representation of how results were derived, that supports defeasible reasoning, has been absent.

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 for 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. We provide algorithmic definitions for these forms of defeasible entailment and prove that the definitions are LM-rational.CATEGORIES: • Theory of computation ~ Automated reasoning • Theory of computation ~ Logic and databases • Computing methodologies ~ Nonmonotonic, default reasoning and belief revision

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 not only the notion of defeasibility, which allows for reasoning about exceptions, but a stronger notion of typicality that is based on defeasibility. KLM-style defeasible reasoning is a logic system that employs defeasibility while Propositional Typicality Logic (PTL) is a logic that does the same for the notion of typicality. Deontic paradoxes are often used to examine logic systems as the paradoxes 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 KLM-style defeasible reasoning and PTL can be used to represent and reason with Forrester’s paradox in such a way as to block undesirable conclusions without completely sacrificing desirable deontic properties.

Free Choice Permission is one of the challenges for the formalisation of norms. In this paper, we follow a novel approach that accepts Free Choice Permission in a restricted form. The intuition behind the guarded form is strongly aligned with the idea of defeasibility. Accordingly, we investigate how to model the guarded form in Defeasible Deontic Logic extended with disjunctive permissions.

The study of defeasible reasoning unites epistemologists with those working in AI, in part, because both are interested in epistemic rationality. While it is traditionally thought to govern the formation and (with)holding of beliefs, epistemic rationality may also apply to the interrogative attitudes associated with our core epistemic practice of inquiry, such as wondering, investigating, and curiosity. Since generally intelligent systems should be capable of rational information-seeking behavior, AI researchers have a natural interest in the norms that govern interrogative attitudes. In this paper, we argue that these norms can be modeled via defeasible inferences to and from questions, i.e. erotetic inferences. We offer a sequent calculus that accommodates the unique features of ``erotetic defeat" and that exhibits the computational properties needed to inform the design of inquisitive systems. The calculus presented here is an improved version of the one presented in Millson (2019), extended to cover a new class of defeasible erotetic inferences.The study of defeasible reasoning unites epistemologists with those working in AI, in part, because both are interested in epistemic rationality. While it is traditionally thought to govern the formation and (with)holding of beliefs, epistemic rationality may also apply to the interrogative attitudes associated with our core epistemic practice of inquiry, such as wondering, investigating, and curiosity. Since generally intelligent systems should be capable of rational inquiry, AI researchers have a natural interest in the norms that govern interrogative attitudes. Following its recent coinage, we use the term “zetetic” to refer to the properties and norms associated with the capacity to inquire. In this paper, we argue that zetetic norms can be modeled via defeasible inferences to and from questions – a.k.a erotetic inferences – in a manner similar to the way norms of epistemic rationality are represented by defeasible inference rules. We offer a sequent calculus that accommodates the unique features of “erotetic defeat" and that exhibits the computational properties needed to inform the design of zetetic agents. The calculus presented here is an improved version of the one presented in (Millson, 2019), extended to cover a new class of defeasible erotetic inferences.

Safety cases are an essential artifact for establishing the safety of complex systems. Industrial use of safety cases varies between industries. Due to inconsistent regulatory guidance, numerous different strategies, notations, and techniques have been developed for safety case construction. Eliminative Argumentation (EA) has been proposed as a technique to systematically improve confidence in a safety case via ‘defeasible reasoning’ wherein reasons to doubt safety claims are introduced and subsequently eliminated. Elimination of doubt results in increased confidence. This paper reports on the application of EA to seven different software-intensive systems in the automotive, rail, and industrial control industries. Our experiences suggest that EA’s doubt-driven approach to safety argumentation increases confidence in a safety case and can be used to support activities such as independent safety assessments and safety verification and validation. From our experiences we synthesized into a set of lessons learned.

Defeasible Description Logics (DDLs) extend Description Logics with defeasible concept inclusions. Reasoning in DDLs often employs rational closure according to the (propositional) KLM postulates. A well-known approach to lift this closure to DDLs is by so-called materialisation. Previously investigated algorithms for materialisation-based reasoning employ reductions to classical reasoning using all Boolean connectors. As a first result in this paper, we present a materialisation-based algorithm for the sub-Boolean DDL , using a reduction to reasoning in classical , rendering materialisation-based defeasible reasoning tractable. The main contribution of this article is a kind of canonical model construction, which can be used to decide defeasible subsumption and instance queries in under rational and the stronger relevant entailment. Our so-called typicality models can reproduce the entailments obtained from materialisation-based rational and relevant closure and, more importantly, obtain stronger versions of rational and relevant entailment. These do not suffer from neglecting defeasible information for concepts appearing nested inside quantifications, which all materialisation-based approaches do. We also show the computational complexity of defeasible subsumption and instance checking in our stronger rational and relevant semantics.

Dealing with context dependent knowledge is a well-known area of study that roots in John McCarthy's seminal work. More recently, the Contextualized Knowledge Repository (CKR) framework has been conceived as a logic-based approach in which knowledge bases have a two layered structure, modeled by a global context and a set of local contexts. The global context not only contains the meta-knowledge defining the properties of local contexts, but also holds the global (context independent) object knowledge that is shared by all of the local contexts. In many practical cases, however, it is desirable to leave the possibility to “override” the global object knowledge at the local level: in other words, it is interesting to recognize the pieces of knowledge that can admit exceptional instances in the local contexts that do not need to satisfy the general axiom. To address this need, we present in this paper an extension of CKR in which defeasible axioms can be included in the global context. The latter are verified in the local contexts only for the instances for which no exception to overriding exists, where exceptions require a justification in terms of facts that are provable from the knowledge base. We formally define this semantics and study some semantic and computational properties, where we characterize the complexity of the major reasoning tasks, among them satisfiability testing, instance checking, and conjunctive query answering. Furthermore, we present a translation of extended CKRs with knowledge bases in the Description Logic SROIQ -RL under the novel semantics to datalog programs under the stable model (answer set) semantics. We also present an implementation prototype and examine its scalability with respect to the size of the input CKR and the amount (level) of defeasibility in experiments. Finally, we compare our representation approach with some major formalisms for expressing defeasible knowledge in Description Logics and contextual knowledge representation. Our work adds to the body of results on using deductive database technology such as SQL and datalog in these areas, and provides an expressive formalism (in terms of intrinsic complexity) for exception handling by overriding.

A prevailing thought is that generics have a covert modal operator at logical form. I claim that if this is right, the covert generic modality is a weak necessity modal. In this paper, I provide evidence for this claim and I sketch a theory. In particular, I will show that there are some important distributional parallels between generics and sentences with overt weak necessity modals: both sorts of sentences share behavior in nonmonotonic reasoning environments and also lack genuine epistemic readings. Acknowledging these parallels and the connection here is in the service of both our understanding of genericity and of weak necessity. Finally, I propose an understanding of generics as involving a covert weak necessity modal and argue that this is a promising path to pursue in relation to different issues related to the interpretation of generics.​ Postprint

We investigate an aspect of defeasibility that has somewhat been overlooked by the non-monotonic reasoning community, namely that of defeasible modes of reasoning. These aim to formalise defeasibility of the traditional notion of necessity in modal logic, in particular of its different readings as action, knowledge and others in specific contexts, rather than defeasibility of conditional forms. Building on an extension of the preferential approach to modal logics, we introduce new modal osperators with which to formalise the notion of defeasible necessity and distinct possibility, and that can be used to represent expected effects, refutable knowledge, and so on. We show how KLM-style conditionals can smoothly be integrated with our richer language. We also propose a tableau calculus which is sound and complete with respect to our modal preferential semantics, and of which the computational complexity remains in the same class as that of the underlying classical modal logic.

Our purpose in this paper is to contribute to a practice-based characterization of scientific inference. We want to explore whether Brandom’s pragmatist–inferentialist framework can suitably accommodate several types of ampliative inference common in scientific reasoning and explanation (probabilistic reasoning, abduction and idealisation). First, we argue that Brandom’s view of induction in terms of merely permissive inferences is inadequate; in order to overcome the shortcoming of Brandom’s proposal, we put forward an alternative conception of inductive, probabilistic reasoning by appeal to the notion of degrees of commitment. Moreover, we examine the sorts of inferential commitments operative in other types of ampliative inferences, such as abduction or reasoning involving idealizations and assumptions. We suggest that agents engaging in these forms of reasoning often undertake restricted inferential commitments, whose scope and reach are more limited that in the case of the commitments associated with full beliefs.

ContextSoftware practitioners are often the primary source of information for software engineering research. They naturally produce information about their experiences of software practice, and the beliefs they infer from their experiences. Researchers must evaluate the quality and quantity of this information for their research. ObjectiveTo examine how concepts and methods from argumentation research can be used to study practitioners evidence, inference and beliefs so as to better understand and improve software practice. MethodWe develop a preliminary framework and preliminary methodology, and use those to identify, extract and structure practitioners evidence, inference and beliefs. We illustrate the application of the framework and methodology with examples from a practitioner's blog post. ResultThe practitioner uses (factual) stories, analogies, examples and popular opinion as evidence, and uses that evidence in defeasible reasoning to justify his beliefs and to rebut the beliefs of other practitioners. ConclusionThe framework, methodology and examples could provide a foundation for software engineering researchers to develop a more sophisticated understanding of, and appreciation for, practitioners defeasible evidence, inference and belief. Further work needs to automate (parts of) the methodology to support larger-scale application of the methodology.

International audience; This demonstration paper introduces DAMN: a defeasible reasoning platform available on the web. It is geared towards decision making where each agent has its own knowledge base that can be combined with other agents to detect and visualize conflicts and potentially solve them using a semantics. It allows the use of different defeasible reasoning semantics (ambiguity blocking/propagating with or without team defeat) and integrates agent collaboration and visualization features.

Recent technological advances have led to unprecedented amounts of generated data that originate from the Web, sensor networks and social media. Analytics in terms of defeasible reasoning - for example for decision making - could provide richer knowledge of the underlying domain. Traditionally, defeasible reasoning has focused on complex knowledge structures over small to medium amounts of data, but recent research efforts have attempted to parallelize the reasoning process over theories with large numbers of facts. Such work has shown that traditional defeasible logics come with overheads that limit scalability. In this work, we design a new logic for defeasible reasoning, thus ensuring scalability by design. We establish several properties of the logic, including its relation to existing defeasible logics. Our experimental results indicate that our approach is indeed scalable and defeasible reasoning can be applied to billions of facts., Under consideration in Theory and Practice of Logic Programming (TPLP)

The paper is motivated by the need of accounting for the practical syllogism as a piece of defeasible reasoning. To meet the need, the paper first refers to ranking theory as an account of defeasible descriptive reasoning. It then argues that two kinds of ought need to be distinguished, purely normative and fact-regarding obligations (in analogy to intrinsic and extrinsic utilities). It continues arguing that both kinds of ought can be iteratively revised and should hence be represented by ranking functions, too, just as iteratively revisable beliefs. Its central proposal will then be that the fact-regarding normative ranking function must be conceived as the sum of a purely normative ranking function and an epistemic ranking function (as suggested in qualitative decision theory). The distinctions defends this proposal with a comparative discussion of some critical examples and some other distinctions made in the literature. It gives a more rigorous justification of this proposal. Finally, it starts developing the logic of purely normative and of fact-regarding normative defeasible reasoning, points to the difficulties of completing the logic of the fact-regarding side, but reaches the initial aim of accounting for the defeasible nature of the practical syllogism. published

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 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.

We investigate Euler diagrammatic systems for defeasible reasoning by extending the usual systems for Euler and Venn diagrams corresponding to standard classical logic. To achieve this, we use the generalized quantifier “most” to formalize defeasible reasoning, as proposed by Schlechta (1995), where defeasible knowledge is represented as “Most A are B” and axioms for “most” are defined. We introduce an Euler diagrammatic system for defeasible reasoning by introducing circle mA that represents “most A” for each circle A. We show that our Euler diagrammatic system is a diagrammatic representation of the symbolic system of the generalized quantifier “most”. Furthermore, we investigate skeptical and credulous strategies in defeasible reasoning with our Euler diagrams.

In this paper we develop a concept aware multi-preferential semantics for dealing with typicality in description logics, where preferences are associated with concepts, starting from a collection of ranked TBoxes containing defeasible concept inclusions. Preferences are combined to define a preferential interpretation in which defeasible inclusions can be evaluated. The construction of the concept-aware multipreference semantics is related to Brewka's framework for qualitative preferences. We exploit Answer Set Programming (in particular, asprin) to achieve defeasible reasoning under the multipreference approach for the lightweight description logic EL+bot. The paper is under consideration for acceptance in TPLP., Comment: Paper presented at the 36th International Conference on Logic Programming (ICLP 2020), University Of Calabria, Rende (CS), Italy, September 2020

This paper provides experimental evidence from German and English against the view that a goal to/zu-PP in combination with a motion verb designates a goal that is reached. We propose that to/zu have a modal meaning, responsible for the defeasibility of the inference that the goal is reached. We argue that the type of subjects (intentional agent vs. accidental agent or theme) determines the flavor of the (necessity) modal encoded by the preposition (teleological or circumstantial), which allows us to account for the observed variation in the strength of the inference with the type of subjects and the type of verbs.

This paper revisits the challenge of Berman and Hafner's "missing link" paper on representing teleological structure in case-based legal reasoning. It is noted that this was mainly an ontological challenge to represent some of what made legal reasoning distinctive, which was given less attention than factual similarity in the dominant AI and Law paradigm, deriving from HYPO. The response to their paper is noted and briefly evaluated. A parallel is drawn to a new challenge to provide deep structure to the legal context of textual meaning, drawing on the forthcoming work of two Constitutional law scholars who appear to place some faith in the ways of thinking that AI and Law has developed.

The purpose of this paper is to analyze the structure and the defeasibility conditions of argument from analogy, addressing the issues of determining the nature of the comparison underlying the analogy and the types of inferences justifying the conclusion. In the dialectical tradition, different forms of similarity were distinguished and related to the possible inferences that can be drawn from them. The kinds of similarity can be divided into four categories, depending on whether they represent fundamental semantic features of the terms of the comparison (essential similarities) or non-semantic ones, indicating possible characteristics of the referents (accidental similarities). Such distinct types of similarity characterize different kinds of analogical arguments, all based on a similar general structure, in which a common genus (or rather a generic feature) is abstracted. Depending on the nature of the abstracted common feature, different rules of inference will apply, guaranteeing the attribution of the analogical predicate to the genus and to the primary subject. This analysis of similarity and the relationship thereof with the rules of inference allows a deeper investigation of the defeasibility conditions.

Reasoning on defeasible knowledge is a topic of interest in the area of description logics, as it is related to the need of representing exceptional instances in knowledge bases. In this direction, in our previous works we presented a framework for representing (contextualized) OWL RL knowledge bases with a notion of justified exceptions on defeasible axioms: reasoning in such framework is realized by a translation into ASP programs. The resulting reasoning process for OWL RL, however, introduces a complex encoding in order to capture reasoning on the negative information needed for reasoning on exceptions. In this paper, we apply the justified exception approach to knowledge bases in \(\textit{DL-Lite}_\mathcal{R}\), i.e. the language underlying OWL QL. We provide a definition for \(\textit{DL-Lite}_\mathcal{R}\) knowledge bases with defeasible axioms and study their semantic and computational properties. The limited form of \(\textit{DL-Lite}_\mathcal{R}\) axioms allows us to formulate a simpler encoding into ASP programs, where reasoning on negative information is managed by direct rules. The resulting materialization method gives rise to a complete reasoning procedure for instance checking in \(\textit{DL-Lite}_\mathcal{R}\) with defeasible axioms.

In recent work, we addressed an important limitation in previous extensions of description logics to represent defeasible knowledge, namely the restriction in the semantics of defeasible concept inclusion to a single preference order on objects of the domain. Syntactically, this limitation translates to a context-agnostic notion of defeasible subsumption, which is quite restrictive when it comes to modelling different nuances of defeasibility. Our point of departure in our recent proposal allows for different orderings on the interpretation of roles. This yields a notion of contextual defeasible subsumption, where the context is informed by a role. In the present paper, we extend this work to also provide a proof-theoretic counterpart and associated results. We define a (naive) tableau-based algorithm for checking preferential consistency of contextual defeasible knowledge bases, a central piece in the definition of other forms of contextual defeasible reasoning over ontologies, notably contextual rational closure.

Linear Logic and Defeasible Logic have been adopted to formalise different features of knowledge representation: consumption of resources, and non monotonic reasoning in particular to represent exceptions. Recently, a framework to combine sub-structural features, corresponding to the consumption of resources, with defeasibility aspects to handle potentially conflicting information, has been discussed in literature, by some of the authors. Two applications emerged that are very relevant: energy management and business process management. We illustrate a set of guide lines to determine how to apply linear defeasible logic to those contexts., Comment: In Proceedings DICE-FOPARA 2019, arXiv:1908.04478. arXiv admin note: substantial text overlap with arXiv:1809.03656

We study the Dung semantics for extended forms of assumption-based argumentation frameworks (ABFs), based on any contrapositive propositional logic, and whose defeasible rules are expressed by arbitrary formulas in that logic. New results on the well-founded semantics for such ABFs are reported, the redundancy of the closure condition is shown, and the use of disjunctive attacks is investigated. Useful properties of the generalized frameworks are also considered.

We propose a solution to the problem of logical omniscience in what we take to be its fundamental version: as concerning arbitrary agents and the knowledge attitude per se. Our logic of knowledge is a spin-off from a general theory of thick content, whereby the content of a sentence has two components: (i) an intension, taking care of truth conditions; and (ii) a topic, taking care of subject matter. We present a list of plausible logical validities and invalidities for the logic of knowledge per se for arbitrary agents, and isolate three explanatory factors for them: (1) the topic-sensitivity of content; (2) the fragmentation of knowledge states; (3) the defeasibility of knowledge acquisition. We then present a novel dynamic epistemic logic that yields precisely the desired validities and invalidities, for which we provide expressivity and completeness results. We contrast this with related systems and address possible objections.

There are well-developed formal and computational theories of argumentation to reason in the face of inconsistency, some with implementations; there are recent efforts to extract arguments from large textual corpora. Both developments are leading towards automated processing and reasoning with inconsistent, linguistically expressed knowledge in order to provide explanations and justifications in a form accessible to humans. However, there remains a gap between the knowledge-bases of computational theories of argumentation, which are generally coarse-grained and semi-structured (e.g. propositional logic), and inferences from knowledge-bases derived from natural language, which are fine-grained and highly structured (e.g. predicate logic). Arguments that occur in textual corpora are very rich, highly various, and incompletely understood. We identify several subproblems which must be addressed in order to bridge the gap, requiring the development of a computational foundation for argumentation coupled with natural language processing. For the computational foundation, we provide a direct semantics, a formal approach for argumentation, which is implemented and suitable to represent and reason with an associated natural language expression for defeasibility. It has attractive properties with respect to expressivity and complexity; we can reason by cases; we can structure higher level argumentation components such as cases and debates. With the implementation, we output experimental results which emphasise the importance of our efficient approach. To motivate our formal approach, we identify a range of issues found in other approaches. For the natural language processing, we adopt and adapt an existing controlled natural language (CNL) to interface with our computational theory of argumentation; the tool takes natural language input and automatically outputs expressions suitable for automated inference engines. A CNL, as a constrained fragment of natural language, helps to control variables, highlights key problems, and provides a framework to engineer solutions. The key adaptation incorporates the expression ‘it is usual that’, which is a plausibly ‘natural’ linguistic expression of defeasibility. This is an important, albeit incremental, step towards the incorporation of linguistic expressions of defeasibility; yet, by engineering such specific solutions, a range of other, relevant issues arise to be addressed. Overall, we can input arguments expressed in a controlled natural language, translate them to a formal knowledge base, represent the knowledge in a rule language, reason with the rules, generate argument extensions, and finally convert the arguments in the extensions into natural language. Our approach makes for fine-grained, highly structure, accessible, and linguistically represented argumentation evaluation. The overall novel contribution of the paper is an integrated, end-to-end argumentation system which bridges a gap between automated defeasible reasoning and a natural language interface. The component novel contributions are the computational theory of ‘direct semantics’, the motivation for our theory, the results with respect to the direct semantics, the implementation, the experimental results, the tie between the formalisation and the CNL, the adaptation of a CNL defeasibility, and an ‘engineering’ approach to fine-grained argument analysis.

Linear Logic and Defeasible Logic have been adopted to formalise different features of knowledge representation: consumption of resources and reasoning with exceptions. We propose a framework to combine sub-structural features, corresponding to the consumption of resources, with defeasibility aspects to handle potentially conflicting information, and we discuss the design choices.

Knowledge based computer systems may be designed for many environments, demonstrating different patterns of behavior. Though the inferences obtained may be similar, the use of the inferences may require some supplementary information directly related to the subject domain properties. For such complex cases a concept of retention is proposed in this paper intended for applications to a wide variety of situations, where an intelligent system may depend upon complex external conditions. Examples of systems designed by the authors are provided that support this new concept. In conclusion, an attempt to formalize this concept in the language of Category Theory is provided.

International audience; In this paper we are interested in the task of a data engineer choosing what tool to use to perform defeasible reasoning with a first order logic knowledge base. To this end we propose the first benchmark in the literature that allows one to classify first order defeasible reasoning tools based on their semantics, expressiveness and performance.

Relations are usually represented in a space of attributes whose values differ only in names similar to algebra of sets. The order of the values or any other preference measures are not significant for such attributes. The paper proposes a mathematical model based on n-tuple algebra (NTA), for relations in which the values of attributes are ordered. For this case, a mathematical tool has been developed that can be used to perform not only the previously discussed methods and means of logical-semantic analysis on the basis of NTA, including analysis of defeasible reasoning and logic-probabilistic analysis, but also to analyze the order and connectivity of structures and implement clustering methods. The concept of granules is introduced, the power of connectivity between the granules is defined, and methods to calculate distances between the disconnected granules are proposed. The obtained dependencies make it possible to extend the scope of classification techniques.