Ensuring reference independence and cautious monotony in abstract argumentation

in International Journal of Approximate Reasoning (2022), 140

In the symbolic artificial intelligence community, abstract argumentation with its semantics, i.e. approaches for defining sets of valid conclusions (extensions) that can be derived from argumentation ... [more ▼]

In the symbolic artificial intelligence community, abstract argumentation with its semantics, i.e. approaches for defining sets of valid conclusions (extensions) that can be derived from argumentation graphs, is considered a promising method for non-monotonic reasoning. However, from a sequential perspective, abstract argumentation-based decision-making processes typically do not guarantee an alignment with common formal notions to assess consistency; in particular, abstract argumentation can, in itself, not enforce the satisfaction of relational principles such as reference independence (based on a key principle of microeconomic theory) and cautious monotony. In this paper, we address this issue by introducing different approaches to ensuring reference independence and cautious monotony in sequential argumentation: a reductionist, an expansionist, and an extension-selecting approach. The first two approaches are generically applicable, but may require comprehensive changes to the corresponding argumentation framework. In contrast, the latter approach guarantees that an extension of the corresponding argumentation framework can be selected to satisfy the relational principle by requiring that the used argumentation semantics is weakly reference independent or weakly cautiously monotonous, respectively, and also satisfies some additional straightforward principles. To highlight the relevance of the approach, we illustrate how the extension-selecting approach to reference independent argumentation can be applied to model (boundedly) rational economic decision-making. [less ▲]

The Law of Evidence and Labelled Deduction: Ten Years Later

in Journal of Applied Logic (2022), 9(4), 887-956

The purpose of this position paper is to reveal, through examples, the potential for collaboration between the theory of legal reasoning on the one hand, and some recently developed instruments of formal ... [more ▼]

The purpose of this position paper is to reveal, through examples, the potential for collaboration between the theory of legal reasoning on the one hand, and some recently developed instruments of formal logic. Three zones of contact are highlighted. 1. The law of evidence, in the light of labelled deductive systems (LDSs), discussed through the example of the admissibility of hearsay evidence. 2. The give and take of legal debate in general, and regarding the acceptability of evidence in particular, represented using the abstract systems of argumentation developed in logic, notably the coloured graphs of BenchCapon. This is considered through an imaginary example. 3. The use of Bayesian networks as tools for analysing the effects of uncertainty on the legal status of actions, illustrated via the same example These three kinds of technique do not exclude each other. On the contrary, many cases of legal argument will need the combined resources of all three. [less ▲]

BTPK-based learning: An Interpretable Method for Named Entity Recognition

E-print/Working paper (2022)

Named entity recognition (NER) is an essential task in natural language processing, but the internal mechanism of most NER models is a black box for users. In some high-stake decision-making areas ... [more ▼]

Named entity recognition (NER) is an essential task in natural language processing, but the internal mechanism of most NER models is a black box for users. In some high-stake decision-making areas, improving the interpretability of an NER method is crucial but challenging. In this paper, based on the existing Deterministic Talmudic Public announcement logic (TPK) model, we propose a novel binary tree model (called BTPK) and apply it to two widely used Bi-RNNs to obtain BTPK-based interpretable ones. Then, we design a counterfactual verification module to verify the BTPK-based learning method. Experimental results on three public datasets show that the BTPK-based learning outperform two classical Bi-RNNs with self-attention, especially on small, simple data and relatively large, complex data. Moreover, the counterfactual verification demonstrates that the explanations provided by the BTPK-based learning method are reasonable and accurate in NER tasks. Besides, the logical reasoning based on BTPK shows how Bi-RNNs handle NER tasks, with different distance of public announcements on long and complex sequences. [less ▲]

The Burden of Persuasion in Abstract Argumentation

in Baroni, Pietro; Benzmüller, Christoph; Wang, Yiqun (Eds.) Logic and Argumentation - 4th International Conference, CLAR 2021 Hangzhou, China, October 20-22, 2021, Proceedings (2021)

In this paper, we provide a formal framework for modeling the burden of persuasion in legal reasoning. The framework is based on abstract argumentation, a frequently studied method of non-monotonic ... [more ▼]

In this paper, we provide a formal framework for modeling the burden of persuasion in legal reasoning. The framework is based on abstract argumentation, a frequently studied method of non-monotonic reasoning, and can be applied to different argumentation semantics; it supports burdens of persuasion with arbitrary many levels, and allows for the placement of a burden of persuasion on any subset of an argumentation framework’s arguments. Our framework can be considered an extension of related works that raise questions on how burdens of persuasion should be handled in some conflict scenarios that can be modeled with abstract argumentation. An open source software implementation of the introduced formal notions is available as an extension of an argumentation reasoning library. [less ▲]

What is Negation in a System 2020?

in IfCoLog Journal of Logics and Their Applications (2021), 8(7), 1977--2034

The notion of negation is basic to any formal or informal logical system. When any such system is presented to us, it is presented either as a system without negation or as a system with some form of ... [more ▼]

The notion of negation is basic to any formal or informal logical system. When any such system is presented to us, it is presented either as a system without negation or as a system with some form of negation. In both cases we are supposed to know intuitively whether there is no negation in the system or whether the form of negation presented in the system is indeed as claimed. To be more specific, suppose Robinson Crusoe writes a logical system with Hilbert type axioms and rules, which includes a unary connective *A. He puts the document in a bottle and let it lose at sea. We find it and take a look. We ask: is the connective "*" a negation in the system? Yet the notion of what is negation in a formal system is not clear. When we see a unary connective *A, (A a wff) together with some other axioms for some additional connectives, how can we tell whether *A is indeed a form of negation of A? Are there some axioms which the connective "*" must satisfy in order to qualify * as a negation? [less ▲]

Explainable Reasoning in Face of Contradictions: From Humans to Machines

in Calvaresi, Davide; Najjar, Amro; Winikoff, Michael (Eds.) et al Explainable and Transparent AI and Multi-Agent Systems - Third International Workshop, EXTRAAMAS 2021, Virtual Event, May 3-7, 2021, Revised Selected Papers (2021)

A well-studied trait of human reasoning and decision-making is the ability to not only make decisions in the presence of contradictions, but also to explain why a decision was made, in particular if a ... [more ▼]

A well-studied trait of human reasoning and decision-making is the ability to not only make decisions in the presence of contradictions, but also to explain why a decision was made, in particular if a decision deviates from what is expected by an inquirer who requests the explanation. In this paper, we examine this phenomenon, which has been extensively explored by behavioral economics research, from the perspective of symbolic artificial intelligence. In particular, we introduce four levels of intelligent reasoning in face of contradictions, which we motivate from a microeconomics and behavioral economics perspective. We relate these principles to symbolic reasoning approaches, using abstract argumentation as an exemplary method. This allows us to ground the four levels in a body of related previous and ongoing research, which we use as a point of departure for outlining future research directions. [less ▲]

Talmudic Norms Approach to Mixtures with a Solution to the Paradox of the Heap: A Position Paper

in Beyond Faith and Rationality (2020)

This paper offers a Talmudic norms solution to the paradox of the heap. The claim is that the paradox arises because philosophers use the wrong language to discuss it. We need a language about objects ... [more ▼]

This paper offers a Talmudic norms solution to the paradox of the heap. The claim is that the paradox arises because philosophers use the wrong language to discuss it. We need a language about objects which is capable of expressing not only the declarative properties of the object (such as being a heap) but also how the object/heap was constructed. Such a view of objects comes from the Talmudic theory of mixtures. To this we add a first attempt at modelling the Talmudic normative theory of mixing (Talmudic calculus of Sorites). We seek a correlation between Talmudic positions on mixtures and philosophical positions on Sorites. The Talmud is very practical and cannot allow for any theoretically unresolved paradox to get in the way, and so it has a lot to offer to philosophy in general and to the heap paradox in particular. [less ▲]

A bimodal simulation of defeasibility in thenormative domain

in CEUR Workshop Proceedings (2020)

In the present work we illustrate how two sorts of defeasiblereasoning that are fundamental in the normative domain, that is, reasoning about exceptions and reasoning about violations, can be simulated ... [more ▼]

In the present work we illustrate how two sorts of defeasiblereasoning that are fundamental in the normative domain, that is, reasoning about exceptions and reasoning about violations, can be simulated via monotonic propositional theories based on a bimodal language with primitive operators representing knowledge and obligation. The proposed theoretical framework paves the way to using native theorem provers for multimodal logic, such as MleanCoP, in order to automate normative reasoning. [less ▲]

Normality, non-contamination and logical depth in classical natural deduction

in Studia Logica (2020), 108(2), 291--357

In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard ... [more ▼]

In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard Gentzen-style natural deduction, (ii) admits of a simple normalization procedure such that normal proofs enjoy the Weak Subformula Property, (iii) provides the means to prove a Non-Contamination Property of normal proofs that is not satisfied by normal proofs in the Gentzen tradition and is useful for applications, especially to formal argumentation, (iv) naturally leads to defining a notion of depth of a proof, to the effect that, for every fixed natural k, normal k-depth deducibility is a tractable problem and converges to classical deducibility as k tends to infinity. [less ▲]

Machine Argumentation. Can We Replace Taxi Drivers by Robots?

in Natural Argument, A tribute to John Woods (2019)

We need ethical non-monotonic action logics to control machines which interact heavily with humans. Such logics face special problems and require features which we need to recognise and to address. We ... [more ▼]

We need ethical non-monotonic action logics to control machines which interact heavily with humans. Such logics face special problems and require features which we need to recognise and to address. We believe that injecting argumentation methods into action pre-conditions is possibly the way to proceed to model what is needed. To get an idea of what is needed we must investigate a typical problem of replacing a human with a robot operating in a highly interactive environment. This paper focuses on replacing a human taxi driver by a robot. Robot driven cars are already under production and so there is an urgent need for modelling the kind of Artificial Intelligence/Logic/Norms/Ethics which is to be involved and installed in the mind of the Robot. This is research in progress. [less ▲]