Multi-agent Argumentation and Dialogue

in IfCoLog Journal of Logics and Their Applications (2022), 9(4), 853-886

In this chapter we give an overview of multi-agent abstract argumentation and dialogue, and its application to formalise legal reasoning. The basis of multi-agent abstract argumentation is input/output ... [more ▼]

In this chapter we give an overview of multi-agent abstract argumentation and dialogue, and its application to formalise legal reasoning. The basis of multi-agent abstract argumentation is input/output argumentation studied by Baroni et al., distinguishing between the individual acceptance of agents and the collective acceptance of the system. The former may also be seen as a kind of conditional reasoning, and the latter may be seen as the reasoning of an external observer. We extend input/output argumentation in two ways. First, we introduce epistemic trust and agent communication, where the former is based on a social network representing epistemic trust, and the latter is based on so-called sub-framework semantics. Second, we introduce dialogue semantics for abstract argumentation by refining agent communication into dialogue steps. A dialogue is a sequence of steps from the framework to the extensions, where in each step of the sequence an agent can commit to accepting some arguments, or commit to hide or reveal one of his rejected arguments. The revealed arguments are then aggregated and an external observer, in our example a judge, can compute which arguments are finally acceptable at a global level. [less ▲]

Detachment in Normative Systems: Examples, Inference Patterns, Properties

in IfCoLog Journal of Logics and Their Applications (2022), 9(4), 1019-1062

There is a variety of ways to reason with normative systems. This partly reflects a variety of semantics developed for deontic logic, such as traditional semantics based on possible worlds, or alternative ... [more ▼]

There is a variety of ways to reason with normative systems. This partly reflects a variety of semantics developed for deontic logic, such as traditional semantics based on possible worlds, or alternative semantics based on algebraic methods, explicit norms or techniques from non-monotonic logic. This diversity raises the question how these reasoning methods are related, and which reasoning method should be chosen for a particular application. In this paper we discuss the use of examples, inference patterns, and more abstract properties. First, benchmark examples can be used to compare ways to reason with normative systems. We give an overview of several benchmark examples of normative reasoning and deontic logic: van Fraassen’s paradox, Forrester’s paradox, Prakken and Sergot’s cottage regulations, Jeffrey’s disarmament example, Chisholm’s paradox, Makinson’s Möbius strip, and Horty’s priority examples. Moreover, we distinguish various interpretations that can be given to these benchmark examples, such as consistent interpretations, dilemma interpretations, and violability interpretations. Second, inference patterns can be used to compare different ways to reason with normative systems. Instead of analysing the benchmark examples semantically, as it is usually done, in this paper we use inference patterns to analyse them at a higher level of abstraction. We discuss inference patterns reflecting typical logical properties such as strengthening of the antecedent or weakening of the consequent. Third, more abstract properties can be defined to compare different ways to reason with normative systems. To define these more abstract properties, we first present a formal framework around the notion of detachment. Some of the ten properties we introduce are derived from the inference patterns, but others are more abstract: factual detachment, violation detection, substitution, replacements of equivalents, implication, para-consistency, conjunction, factual monotony, norm monotony, and norm induction. We consider these ten properties as desirable for a reasoning method for normative systems, and thus they can be used also as requirements for the further development of formal methods for normative systems and deontic logic. [less ▲]

Preface - Journal of Applied Logics

in IfCoLog Journal of Logics and Their Applications (2021), 8(6), 1335-1338

Åqvist's Dyadic Deontic Logic E in HOL

in IfCoLog Journal of Logics and Their Applications (2019), 6(5), 733--755

Rights and Punishment: The Hohfeldian Theory’s Applicability and Morals in Understanding Criminal Law

in IfCoLog Journal of Logics and Their Applications (2019)

A Case Study On Computational Hermeneutics: E. J. Lowe's Modal Ontological Argument

in IfCoLog Journal of Logics and Their Applications (2018), 5(7), 1567-1603

Computers may help us to better understand (not just verify) arguments. In this article we defend this claim by showcasing the application of a new, computer-assisted interpretive method to an exemplary ... [more ▼]

Computers may help us to better understand (not just verify) arguments. In this article we defend this claim by showcasing the application of a new, computer-assisted interpretive method to an exemplary natural-language argument with strong ties to metaphysics and religion: E. J. Lowe’s modern variant of St. Anselm’s ontological argument for the existence of God. Our new method, which we call computational hermeneutics, has been particularly conceived for use in interactive-automated proof assistants. It aims at shedding light on the meanings of words and sentences by framing their inferential role in a given argument. By employing automated theorem reasoning technology within interactive proof assistants, we are able to drastically reduce (by several orders of magnitude) the time needed to test the logical validity of an argument’s formalization. As a result, a new approach to logical analysis, inspired by Donald Davidson’s account of radical interpretation, has been enabled. In computational hermeneutics, the utilization of automated reasoning tools effectively boosts our capacity to expose the assumptions we indirectly commit ourselves to every time we engage in rational argumentation and it fosters the explicitation and revision of our concepts and commitments. [less ▲]

Detachment in Normative Systems: Examples, inference Patterns, Properties

in IfCoLog Journal of Logics and Their Applications (2017), 4(9), 2295-3039

There is a variety of ways to reason with normative systems. This partly reflects a variety of semantics developed for deontic logic, such as traditional semantics based on possible worlds, or alternative ... [more ▼]

There is a variety of ways to reason with normative systems. This partly reflects a variety of semantics developed for deontic logic, such as traditional semantics based on possible worlds, or alternative semantics based on algebraic methods, explicit norms or techniques from non-monotonic logic. This diversity raises the question how these reasoning methods are related, and which reasoning method should be chosen for a particular application. In this paper we discuss the use of examples, inference patterns, and more abstract properties. First, benchmark examples can be used to compare ways to reason with normative systems. We give an overview of several benchmark examples of normative reasoning and deontic logic: van Fraassen’s paradox, Forrester’s paradox, Prakken and Sergot’s cottage regulations, Jeffrey’s disarmament example, Chisholm’s paradox, Makinson’s Möbius strip, and Horty’s priority examples. Moreover, we distinguish various interpretations that can be given to these benchmark examples, such as consistent interpretations, dilemma interpretations, and violability interpretations. Second, inference patterns can be used to compare different ways to reason with normative systems. Instead of analysing the benchmark examples semantically, as it is usually done, in this paper we use inference patterns to analyse them at a higher level of abstraction. We discuss inference patterns reflecting typical logical properties such as strengthening of the antecedent or weakening of the consequent. Third, more abstract properties can be defined to compare different ways to reason with normative systems. To define these more abstract properties, we first present a formal framework around the notion of detachment. Some of the ten properties we introduce are derived from the inference patterns, but others are more abstract: factual detachment, violation detection, substitution, replacements of equivalents, implication, para-consistency, conjunction, factual monotony, norm monotony, and norm induction. We consider these ten properties as desirable for a reasoning method for normative systems. [less ▲]

Handling Norms in Multi-Agent System by Means of Formal Argumentation

in IfCoLog Journal of Logics and Their Applications (2017)

Formal argumentation is used to enrich and analyse normative multi-agent systems in various ways. In this chapter, we discuss three examples from the literature of handling norms by means of formal ... [more ▼]

Formal argumentation is used to enrich and analyse normative multi-agent systems in various ways. In this chapter, we discuss three examples from the literature of handling norms by means of formal argumentation. First, we discuss how existing ways to resolve conflicts among norms using priorities can be represented in formal argumentation, by showing that the so-called Greedy and Reduction approaches can be represented using the weakest and the last link principles respectively. Based on such representation results, formal argumentation can be used to explain the detachment of obligations and permissions from hierarchical normative systems in a new way. Second, we discuss how formal argumentation can be used as a general theory for developing new approaches for normative reasoning, using a dynamic ASPIC-based legal argumentation theory. We show how existing logics of normative systems can be used to analyse such new argumentation systems. Third, we show how argumentation can be used to reason about other challenges in the area of normative multiagent systems as well, by discussing a model for arguing about legal interpretation. In particular, we show how fuzzy logic combined with formal argumentation can be used to reason about the adoption of graded categories and thus address the problem of open texture in normative interpretation. Our aim to discuss these three examples is to inspire new applications of formal argumentation to the challenges of normative reasoning in multiagent systems. [less ▲]

Reasoning under the Influence of Universal Distortion. Sex Offenders Case Study

in IfCoLog Journal of Logics and Their Applications (2017)

We define and study the phenomenon of a universal distortion into a reasoning system or an argumentation network. Such distortions can happen for various reasons, for instance under the influence of ... [more ▼]

We define and study the phenomenon of a universal distortion into a reasoning system or an argumentation network. Such distortions can happen for various reasons, for instance under the influence of alcohol or a fundamentalist religion, or as the result of a behavioural disorder such as paedophilia. We define the notion theoretically in the framework of abstract argumentation and present an actual case study of a sex offender. We then present a formal logical model. [less ▲]

Implicit dynamic function introduction and Ackermann-like Function Theory

in IfCoLog Journal of Logics and Their Applications (2017)

We discuss a feature of the natural language of mathematics – the implicit dynamic introduction of functions – that has, to our knowledge, not been captured in any formal system so far. If this feature is ... [more ▼]

We discuss a feature of the natural language of mathematics – the implicit dynamic introduction of functions – that has, to our knowledge, not been captured in any formal system so far. If this feature is used without limitations, it yields a paradox analogous to Russell’s paradox. Hence any formalism capturing it has to impose some limitations on it. We sketch two formalisms, both extensions of Dynamic Predicate Logic, that innovatively do capture this feature, and that differ only in the limitations they impose onto it. One of these systems is based on Ackermann-like Function Theory, a novel foundational theory of functions that is inspired by Ackermann Set Theory and that interprets ZFC. [less ▲]