In this paper we provide a detailed analysis of the inference process induced by logical argumentation frameworks. The frameworks may be defined with respect to any propositional language and logic, different arguments that represent deductions in the logic, various support-based attack relations between arguments, and all the complete Dung-style semantics for the frameworks. We show that, ultimately, for characterizing the inference process with respect to a given framework, extension-based semantics may be divided into two types: single-extension and multiple-extension, which induce respective kinds of entailment relations. These entailments are further classified by the way they tolerate new information (nonmonotonicity-related properties) and maintain conflicts among arguments (inconsistency-related properties). Moreover, we show how the entailments induced by reasoning on the basis of maximal consistency, by Makinson’s default assumptions and by adaptive logics correspond to the entailments induced by specific classes of logical argumentation frameworks.

Default logic and formal argumentation are paradigmatic methods in the study of nonmonotonic inference. Defeasible information often comes in different strengths stemming from different degrees of reliability in epistemic applications or from varying strengths of authorities issuing norms in deontic applications. In both paradigms methods have been developed to deal with prioritized knowledge bases. Questions of comparability of these methods therefore naturally arise. Argumentation theory has been developed with a strong emphasis on unification. It is therefore a desideratum to obtain natural representations of various approaches to (prioritized) default logic within frameworks of structured argumentation, such as ASPIC. Important steps in this direction have been presented in Liao et al. (2016, 2018). In this work we identify and address some problems in earlier translations, we broaden the focus from total to modular orderings of defaults, and we consider non-normal defaults.

In this paper we study formal properties of approaches to the reasoning with prioritized defeasible assumptions. We focus on methods proposed in formal argumentation, more specifically in the context of assumption- based argumentation.

We systematically compare two approaches for handling conflicts: pref- erence-based defeats and preference-based defeats extended with reverse defeat. We investigate under which conditions these approaches give rise to the same output. We study several meta-theoretical properties includ- ing argumentation theoretical properties (such as Dung’s Fundamental Lemma and the consistency of extensions) and properties for nonmono- tonic reasoning (such as Cautious Monotony and Cut) in a parametrized way, i.e., relative to specific constraints on the underlying deducability relation. Finally, we study the relationship between these approaches and preferred subtheories, a nonmonotonic reasoning formalism that is based on maximal consistent subsets of a totally ordered knowledge base.

In the parametrized setting we study different sub-classes of assumption- based argumentation frameworks. For instance, we identify a particularly well-behaved sub-class of argumentation-based frameworks for which the different conflict-handling mechanisms coincide, which give the same out- comes as preferred subtheories and for which core properties of nonmono- tonic logic are valid.

Keywords: structured argumentation; abstract argumentation; non- monotonic logic; defeasible reasoning; preferred subtheories; maximal consistent sets; preferences; priorities; 1 Introduction

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 LC, the modal logic S5, and the relevance logic RM), 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.

Formal models of scientific inquiry, aimed at capturing socio-epistemic aspects underlying the process of scientific research, have become an important method in formal social epistemology and philosophy of science. In this introduction to the special issue we provide a historical overview of the development of formal models of this kind and analyze their methodological contributions to discussions in philosophy of science. In particular, we show that their significance consists in different forms of `methodological iteration’ (Elliott, 2012) whereby the models initiate new lines of inquiry, isolate and clarify problems with existing knowledge claims, and stimulate further research.

Structured argumentation is a family of formal approaches for the handling of defeasible, potentially inconsistent information. Many models for structured argumentation distinguish between strict and defeasible inference rules. Defeasible rules often come with varying degrees of strength which is formally represented by a preorder over the defeasible rules. Various lifting principles have been presented in the literature to determine the relative strength of an argument by considering the strength of the defeasible rules used in its construction. The strength of arguments then comes into play when determining whether an attack (a purely syntactic relationship between arguments) results in a defeat (i.e. a successful attack). In \cite{caminada2007evaluation,Wu-Phd}, several rationality postulates were proposed that serve as a measure to assess the normative rationality of structured argumentation formalisms. In \cite{heyninck2017revisiting}, the first formalism satisfying all rationality postulates for structured argumentation when taking into account totally ordered defeasible rules was proposed. In many settings, assuming a total order greatly limits the realistic modelling capabilities of a formal system, e.g. when agents do not know the actual preferences of each rule or since different agents have different preferences over defeasible rules. Our paper shows that in the more general setting of preorders, violations of several rationality postulates can occur. We show how for a wide class of lifting principles, these violations can be avoided, resulting in the first Dung-based system that satisfies all four rationality postulates for preordered defeasible rule bases.

In this paper we provide a proof theoretical investigation of logical argumentation, where arguments are represented by sequents, conflicts between arguments are represented by sequent elimination rules, and deductions are made by dynamic proof systems extending standard sequent calculi. The idea is to imitate argumentative movements in which certain claims are introduced or withdrawn in the presence of counter-claims. This is done by a dynamic evaluation of sequences of sequents, in which the latter are considered `derived’ or `not derived’ according to the content of the sequence. We show that decisive conclusions of such a process correspond to well-accepted consequences of the underlying argumentation framework. The outcome is therefore a general and modular proof-theoretical approach for paraconsistent and non-monotonic reasoning with argumentation systems.

Recent studies of scientific interaction based on agent-based models (ABMs) suggest that a crucial factor conducive to efficient inquiry is what \cite{zollman2010epistemic} has dubbed `transient diversity’. It signifies a process in which a community engages in parallel exploration of rivaling theories lasting sufficiently long for the community to identify the best theory and to converge on it. But what exactly generates transient diversity? And is transient diversity a decisive factor when it comes to the efficiency of inquiry? In this paper we examine the impact of different conditions on the efficiency of inquiry, as well as the relation between diversity and efficiency. This includes certain diversity-generating mechanisms previously proposed in the literature (such as different social networks and cautious decision-making), as well as some factors that have so far been neglected (such as evaluations underlying theory-choice performed by scientists).

This study is obtained via an argumentation-based ABM (\cite{ArgABM-HSR,ABM-Lori}). Our results suggest that cautious decision-making does not always have a significant impact on the efficiency of inquiry while different evaluations underlying theory-choice and different social networks do. Moreover, we find a correlation between diversity and a successful performance of agents only under specific conditions, which indicates that transient diversity is sometimes not the primary factor responsible for efficiency. Altogether, when comparing our results to those obtained by structurally different ABMs based on Zollman’s work, the impact of specific factors on efficiency of inquiry, as well as the role of transient diversity in achieving efficiency, appear to be highly dependent on the underlying model.

In this paper I examine the problem of inconsistency toleration in the context of scientific pluralism. I argue that, first of all, the notion of in consistency toleration has to be qualified with respect to the evaluative attitude that one takes towards a given scientific theory or theories. Second, I show which types of inconsistency toleration are compatible with two major approaches to scientific pluralism, the so-called modest and the radical one. In view of this I suggest some points of demarcation between these two approaches.

The aim of this paper is to outline a first-order model for ampliative reasoning that fruitfully combines the inference patterns of inductive generalization and factual abduction. The pattern of inductive generalization is the archetype pattern of inductive inference by which we arrive at a universally quantified statement (All Ps are Q) given one or more instances (Some Ps are Q). In factual abduction, we reason from a universally quantified statement (All Ps are Q) and an instance of its consequent (object a is Q) to an instance of its antecedent (object a is P). It is shown how these patterns can be combined in such a way that inductively inferred generalizations can be used as premises in abductive inferences, and that conclusions of abductive inferences in turn can be used to inductively infer new generalizations. This process is formally explicated within the adaptive logics framework in terms of a preferential model semantics.

We present a formal argumentation system for dealing with the detachment of prioritized conditional obligations and permissions. In the presence of facts and constraints, we answer the question whether an unconditional obligation or permission is detachable by considering arguments for and against its detachment. For the evaluation of arguments in favour of detachment, we use a Dung-style argumentation-theoretical semantics. We illustrate how violations and contrary-to-duty scenarios are dealt with in our framework, and pay special attention to conflict-resolution via priorities.

In this paper we introduce hypersequent-based frameworks for the modeling of defeasible reasoning by means of logic-based argumentation. These frameworks are an extension of sequent-based argu- mentation frameworks, in which arguments are represented not only by sequents, but by more general expressions, called hypersequents. This generalization allows us to overcome some of the weaknesses of logical argumentation reported in the literature and to prove several desirable properties, stated in terms of rationality postulates. For this, we take the relevance logic RM as the deductive base of our formalism. This logic is regarded as “by far the best understood of the Anderson-Belnap style systems” (Dunn & Restall, Handbook of Philosophical Logic, Vol.6). It has a clear semantics in terms of Sugihara matrices, as well as sound and com- plete Hilbert- and Gentzen-type proof systems. The latter are defined by hypersequents and admit cut elimination. We show that hypersequent-based argumentation yields a robust defeasible variant of RM with many desirable properties.