Defeasible Rules Research Articles

Which are the true defeasible logics?

The class of defeasible logics is only vaguely defined – it is defined by a few exemplars and the general idea of efficient reasoning with defeasible rules. The recent definition of the defeasible logic DL ( ∂ | | ) introduced new features to such logics, which have repercussions that we explore. In particular, we define a class of logics that accommodates the new logic while retaining the traditional properties of defeasible logics.

Argument strength in probabilistic argumentation based on defeasible rules

It is common for people to remark that a particular argument is a strong (or weak) argument. Having a handle on the relative strengths of arguments can help in deciding on which arguments to consider, which arguments to regard as acceptable, and on which arguments to present to others in a discussion. In computational models of argument, there is a need for a deeper understanding of argument strength. It is a multidimensional problem, and in this paper, we focus on one aspect of argument strength for deductive argumentation based on a defeasible logic. We assume a probability distribution over models of the language and consider how there are various ways to calculate argument strength based on the probabilistic necessity and sufficiency of the premises for the claim, the probabilistic sufficiency of competing premises the claim, and the probabilistic necessity of the premises for competing claims. We provide axioms for characterizing probability-based measures of argument strength, and we investigate four specific probability-based measures.

Normal forms of conditional knowledge bases respecting system P-entailments and signature renamings

Conditionals are defeasible rules of the form If A then usually B, and they play a central role in many approaches to nonmonotonic reasoning. Normal forms of conditional knowledge bases consisting of a set of such conditionals are useful to create, process, and compare the knowledge represented by them. In this article, we propose several new normal forms for conditional knowledge bases. Compared to the previously introduced antecedent normal form, the reduced antecedent normal form (RANF) represents conditional knowledge with significantly fewer conditionals by taking nonmonotonic entailments licenced by system P into account. The renaming normal form(ρNF) addresses equivalences among conditional knowledge bases induced by renamings of the underlying signature. Combining the concept of renaming normal form with other normal forms yields the renaming antecedent normal form (ρ ANF) and the renaming reduced antecedent normal form (ρ RANF). For all newly introduced normal forms, we show their key properties regarding, existence, uniqueness, model equivalence, and inferential equivalence, and we develop algorithms transforming every conditional knowledge base into an equivalent knowledge base being in the respective normal form. For the most succinct normal form, the ρ RANF, we present an algorithm KBρra systematically generating knowledge bases over a given signature in ρ RANF. We show that the generated knowledge bases are consistent, pairwise not antecedentwise equivalent, and pairwise not equivalent under signature renaming. Furthermore, the algorithm is complete in the sense that, when taking signature renamings and model equivalence into account, every consistent knowledge base is generated. Observing that normalizing the set of all knowledge bases over a signature Σ to ρ RANF yields exactly the same result as KBρra (Σ), highlights the interrelationship between normal form transformations on the one hand and systematically generating knowledge bases in normal form on the other hand.

Health Support System for Diabetes Prevention Using IoT and Networked Health Monitoring Equipment

For participants of diabetes prevention programs, we consider that it is effective to record vital signs, such as weight and blood pressure, and to receive instruction based on such readings during the follow-up period in order to avoid rebound. Although the Internet is an effective medium for recording data and reporting everyday health status, health support systems that require the use of a PC can place a heavy burden on users, especially elderly users. In this research, we utilized a sensor information web service which is a home network based on ZigBee, and discuss effective implementation of a follow-up system. We explained and demonstrated the proposed system to participants who had completed a diabetes prevention program and administered a questionnaire about their impression of system use. From the questionnaire results, we clarify the considerations and requirements necessary for introducing such a home network system with the elderly. The ultimate purpose of this paper is providing to provide a standard knowledge base system toward a medical prescription capable of dealing with(inconsistencies) and exceptions cases, which will enhance individual healthcare and provide an appropriate prescription. This is accomplished by expanding the capabilities of description logic with defeasible rules, to achieve accurate prescription decision for any patient’s condition(s).

Devising the set of abnormalities for a given defeasible rule

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.

Rationality and maximal consistent sets for a fragment of ASPIC + without undercut

Structured argumentation formalisms, such as ASPIC + , offer a formal model of defeasible reasoning. Usually such formalisms are highly parametrized and modular in order to provide a unifying framework in which different forms of reasoning can be expressed. This generality comes at the price that, in their most general form, formalisms such as ASPIC + do not satisfy important rationality postulates, such as non-interference. Similarly, links to other forms of knowledge representation, such as reasoning with maximal consistent sets of rules, are insufficiently studied for ASPIC + although such links have been established for other, less complex forms of structured argumentation where defeasible rules are absent. Clearly, for a formal model of defeasible reasoning it is important to understand for which range of parameters the formalism (a) displays a behavior that adheres to common standards of consistency, logical closure and logical relevance and (b) can be adequately described in terms of other well-known forms of knowledge representation. In this paper we answer this question positively for a fragment of ASPIC + without the attack form undercut by showing that it satisfies all standard rationality postulates of structured argumentation under stable and preferred semantics and is adequate for reasoning with maximal consistent sets of defeasible rules. The study is general in that we do not impose any other requirements on the strict rules than to be contrapositable and propositional and in that we also consider priorities among defeasible rules, as long as they are ordered by a total preorder and lifted by weakest link. In this way we generalize previous similar results for other structured argumentation frameworks and so shed further light on the close relations between assumption-based argumentation and ASPIC + .

On the Logical Foundation of a Personalized Medical Prescription System

This paper, lays down the logical foundations for a personalized medical prescription system. The proposed system employs detailed pharmaceutical and medical knowledge about a medication and its effects or side effects on the patient, which may go beyond what is available in medication leaflets. The ontology was initially built for the proposed system and employs the description logic system, ALC, for knowledge representation. However, the uncertain nature of medical and medicinal knowledge poses some problems such as drug-drug interactions and drug-disease interactions, which render ALC inadequate to represent and reason within a system such as a personalized medical prescription system. Indeed, there is a need for a more flexible representation that allows reasoning with incomplete knowledge and possibly inconsistent cases. ALC is extended with defeasible rules to obtain defeasible ALC. Defeasible ALC allows the prevention of adverse drug interactions, detection drug-drug interactions and detection of drug-disease interactions. The ultimate purpose of this paper is providing to provide a standard knowledge base system toward a medical prescription capable of dealing with incomplete knowledge, conflicting information (inconsistencies) and exceptions cases, which will enhance individual healthcare and provide an appropriate prescription. This is accomplished by expanding the capabilities of description logic with defeasible rules, to achieve an accurate prescription decision for any patient’s condition(s). Once implemented, a personalized medical prescription system intends to assist, not to replace, the clinician during medical prescription(s) or the pharmacist(s).

Research on the Path of Science and Technology Supporting the Construction of Jiangsu Modern Marine Economic System

Song, S.; Wang, X., and Su, C., 2019. Research on the path of science and technology supporting the construction of Jiangsu modern marine economic system. In: Li, L.; Wan, X.; and Huang, X. (eds.), Recent Developments in Practices and Research in Coastal Regions: Transportation, Environment, and Economy, Journal of Coastal Research, Special Issue No. 98, pp. 179–182. Coconut Creek (Florida), ISSN 0749-0208.Research on the construction path of marine economic system is a kind of exploration of behavior based on data flow among the regional economies in the Inner Mongolia area. In this paper, the Dijstra algorithm is combined to explore the regional economic development gap and the coordinated development path in the Inner Mongolia area. Through several preconditions and a conclusion, the defeasible rule for the effective tender can be obtained. In addition, the process of deduction is explored through the dialogue tree. Verification and analysis on the algorithm are carried out through instances. The final result shows that, for the Jiangsu modern marine economy, the algorithm put forward in this paper can be used to implement exploration on the regional economic development gap and the coordinated development path in the Inner Mongolia area.

Arguing about causes in law: a semi-formal framework for causal arguments

Disputes over causes play a central role in legal argumentation and liability attribution. Legal approaches to causation often struggle to capture cause-in-fact in complex situations, e.g. overdetermination, preemption, omission. In this paper, we first assess three current theories of causation (but-for, NESS, ‘actual causation’) to illustrate their strengths and weaknesses in capturing cause-in-fact. Secondly, we introduce a semi-formal framework for modelling causal arguments through strict and defeasible rules. Thirdly, the framework is applied to the Althen vaccine injury case. And lastly, we discuss the need for new criteria based on a common causal argumentation framework and propose ideas on how to integrate the current theories of causation to assess the strength of causal arguments, while also acknowledging the tension between evidence-based and policy-based causal analysis in law.

Converness: Ontology‐driven conversational awareness and context understanding in multimodal dialogue systems

AbstractDialogue‐based systems often consist of several components, such as communication analysis, dialogue management, domain reasoning, and language generation. In this paper, we present Converness, an ontology‐driven, rule‐based framework to facilitate domain reasoning for conversational awareness in multimodal dialogue‐based agents. Converness uses Web Ontology Language 2 (OWL 2) ontologies to capture and combine the conversational modalities of the domain, for example, deictic gestures and spoken utterances, fuelling conversational topic understanding, and interpretation using description logics and rules. At the same time, defeasible rules are used to couple domain and user‐centred knowledge to further assist the interaction with end users, facilitating advanced conflict resolution and personalised context disambiguation. We illustrate the capabilities of the framework through its integration into a multimodal dialogue‐based agent that serves as an intelligent interface between users (elderly, caregivers, and health experts) and an ambient assistive living platform in real home settings.

A formal characterization of the outcomes of rule-based argumentation systems

Rule-based argumentation systems are developed for reasoning about defeasible information. As a major feature, their logical language distinguishes between strict rules (encoding strict information) and defeasible rules (describing general behavior with exceptional cases). They build arguments by chaining such rules, define attacks between them, use a semantics for evaluating the arguments and finally identify the plausible conclusions that follow from the rules. Focusing on the family of inconsistency-based attack relations, this paper presents the first study of the outcomes of such systems under various acceptability semantics, namely naive, stable, semi-stable, preferred, grounded and ideal. It starts by extending the existing list of rationality postulates that any rule-based system should satisfy. Then, it defines the key notion of option of a theory (a theory being a set of facts, a set of strict rules and a set of defeasible rules). For each of the cited semantics, it characterizes the extensions of a rule-based system that satisfies all the postulates in terms of options of the theory under which the system is built. It also fully characterizes the set of plausible conclusions of the system. The results show that designing a rule-based argumentation system requires great care.

Fundamental properties of attack relations in structured argumentation with priorities

Due to a proliferation and diversity of approaches to structured argumentation with prioritized rules, several simple and intuitive principles for characterization and evaluation of the proposed attack relations have recently been introduced in [23]. While the proposed principles and properties are helpful, they do not identify unique attack relations. Any user of structured argumentation still faces a fundamental problem of determining an appropriate attack relation for her/his application and further principles that could help in identifying such attack relation.We argue that a key purpose of introducing priorities between defeasible rules is to remove undesired attacks while keeping the set of removed attacks to a minimum. This intuitive idea could be viewed as a kind of minimal-removal-principle. We show in this paper that the minimal-removal-principle together with a new simple and intuitive property of inconsistency-resolving and previously proposed properties indeed characterize a unique attack relation referred to as the canonical attack relation. We show that canonical attack relations could be characterized in three distinct ways, as the supremum of a complete upper-semilattice of regular attack relations, or by removing the undesired attacks from the basic attack relations where the undesired attacks are captured by a least-fixed point of an intuitive removal function, or as the normal attack relations introduced in an earlier paper for a class of well-prioritized knowledge bases.We start our study with a language consisting only of literals and two type of attacks, rebut and undercut. We then show that our approach can easily be scaled up by showing that all key results still hold for general underlying logical languages and the inclusion of assumptions.We apply our proposed approach to valued-based argumentation and show that it also leads to the canonical semantics.

Relating Concrete Defeasible Reasoning Formalisms and Abstract Argumentation

There are a wide variety of formalisms for defeasible reasoning that can be seen as implementing concrete argumentation on defeasible rules. However there has been little work on the relationship between such languages and Dung’s abstract argumentation. In this paper we identify two small fragments of defeasible rule languages on which many concrete defeasible formalisms agree. The two fragments are closely related, as we show. Both arise as ways to express abstract argumentation frameworks in the concrete formalisms. Using these fragments, we establish a close relationship between abstract argumentation under semantics based on complete extensions, and ambiguity blocking logics in the framework of Antoniou et al. These results support a uniform approach to deriving complexity lower bounds for defeasible formalisms, where a lower bound is established for abstract argumentation and can then be extended “for free” to corresponding concrete defeasible formalisms.

An argumentation system for defeasible reasoning

Rule-based argumentation systems are developed for reasoning about defeasible information. They take as input a theory made of a set of facts, a set of strict rules, which encode strict information, and a set of defeasible rules which describe general behavior with exceptional cases. They build arguments by chaining such rules, define attacks between them, use a semantics for evaluating the arguments, and finally identify the plausible conclusions that follow from the theory.Undercutting is one of the main attack relations of such systems. It consists of blocking the application of defeasible rules when their exceptional cases hold. In this paper, we consider this relation for capturing all the different conflicts in a theory. We present the first argumentation system that uses only undercutting, and show that it satisfies the rationality postulates proposed in the literature. Finally, we fully characterize both its extensions and its plausible conclusions under various acceptability semantics. Indeed, we show full correspondences between extensions and sub-theories of the theory under which the argumentation system is built.

Two Aspects of Relevance in Structured Argumentation: Minimality and Paraconsistency

This paper studies two issues concerning relevance in structured argumentation in the context of the ASPIC+ framework, arising from the combined use of strict and defeasible inference rules. One issue arises if the strict inference rules correspond to classical logic. A longstanding problem is how the trivialising effect of the classical Ex Falso principle can be avoided while satisfying consistency and closure postulates. In this paper, this problem is solved by disallowing chaining of strict rules, resulting in a variant of the ASPIC+ framework called ASPIC*, and then disallowing the application of strict rules to inconsistent sets of formulas. Thus in effect Rescher & Manor's paraconsistent notion of weak consequence is embedded in ASPIC*. Another issue is minimality of arguments. If arguments can apply defeasible inference rules, then they cannot be required to have subset-minimal premises, since defeasible rules based on more information may well make an argument stronger. In this paper instead minimality is required of applications of strict rules throughout an argument. It is shown that under some plausible assumptions this does not affect the set of conclusions. In addition, circular arguments are in the new ASPIC* framework excluded in a way that satisfies closure and consistency postulates and that generates finitary argumentation frameworks if the knowledge base and set of defeasible rules are finite. For the latter result the exclusion of chaining of strict rules is essential. Finally, the combined results of this paper are shown to be a proper extension of classical-logic argumentation with preferences and defeasible rules.

Two aspects of relevance in structured argumentation

This paper studies two issues concerning relevance in structured argumentation in the context of the ASPIC+ framework, arising from the combined use of strict and defeasible inference rules. One is...

An OWL ontology library representing judicial interpretations

The article introduces JudO, an OWL2 ontology library of legal knowledge that relies on the metadata contained in judicial documents. JudO represents the interpretations performed by a judge while conducting legal reasoning towards the adjudication of a case. To the aim of this application, judicial interpretation is intended in the restricted sense of the acts of judicial subsumption performed by the judge when he considers a material instance (token in Searle's terminology), and assigns it to an abstract category (type). The ontology library is based on a theoretical model and on some specific patterns that exploit some new features introduced by OWL2. JudO provides meaningful legal semantics, while retaining a strong connection to source documents (fragments of legal texts). The application task is to enable detection and modeling of jurisprudence-related information directly from the text, and to perform shallow reasoning on the resulting knowledge base. The ontology library is also supposed to support a defeasible rule set for legal argumentation on the groundings of judicial decisions.

A structured argumentation system with backing and undercutting

This work introduces Extended Defeasible Logic Programming (E-DeLP), a structured argumentation system enabling the expression of reasons for and against using defeasible rules. E-DeLPextends the formalism of Defeasible Logic Programming (DeLP) by incorporating two new kinds of rules: backing and undercutting rules. In that way, E-DeLPaccounts for Toulmin׳s notion of backing and Pollock׳s notion of undercut, two important contributions within the field of argumentation. Thus, E-DeLPconstitutes a novel approach, being the first structured argumentation system in providing a unified setting for modeling Toulmin׳s and Pollock׳s ideas simultaneously.

Formalisation and logical properties of the maximal ideal recursive semantics for weighted defeasible logic programming

Possibilistic defeasible logic programming (P-DeLP) is a logic programming framework which combines features from argumentation theory and logic programming, in which defeasible rules are attached with weights expressing their relative belief or preference strength. In P-DeLP,a conclusion succeeds if there exists an argument that entails the conclusion and this argument is found to be undefeated by a warrant procedure that systematically explores the universe of arguments in order to present an exhaustive synthesis of the relevant chains of pros and cons for the given conclusion. Recently, we have proposed a new warrant recursive semantics for P-DeLP, called Recursive P-DeLP (RP-DeLP for short), based on the claim that the acceptance of an argument should imply also the acceptance of all its sub-arguments which reflect the different premises on which the argument is based. This paper explores the relationship between the exhaustive dialectical analysis-based semantics of P-DeLP and the recursive-based semantics of RP-DeLP, and analyses a non-monotonic inference operator for RP-DeLP which models the expansion of a given program by adding new weighted facts associated with warranted conclusions. Given the recursive-based semantics of RP-DeLP, we have also implemented an argumentation framework for RP-DeLP that is able to compute not only the output of warranted and blocked conclusions, but also explain the reasons behind the status of each conclusion. We have developed this framework as a stand-alone application with a simple text-based input/output interface to be able to use it as part of other artificial intelligence systems.

A Dialogue System for Coherent Reasoning with Inconsistent Knowledge Bases

Traditionally, the AI community assumes that a knowledge base must be consistent. Despite that, there are many applications where, due to the existence of rules with exceptions, inconsistent knowledge must be considered. One way of restoring consistency is to withdraw conflicting rules; however, this will destroy part of the knowledge. Indeed, a better alternative would be to give precedence to exceptions. This paper proposes a dialogue system for coherent reasoning with inconsistent knowledge, which resolves conflicts by using precedence relations of three kinds: explicit precedence relation, which is synthesized from precedence rules; implicit precedence relation, which is synthesized from defeasible rules; mixed precedence relation, which is synthesized by combining explicit and implicit precedence relations.