On Gilbert’s multi-modal theory of argumentation, the “logical” is but one among many modes of argument, including the emotional, the visceral (physical), and the kisceral (intuitive). Yet, I argue that, properly understood, the logical is not one mode among many. Rather, it is better understood as the _uber-mode_ of argument. What Gilbert calls the “logical mode” of argument—a linear, orderly, highly verbalizable, way of arguing—is made possible only to the extent that the logic of some space of reasons has (...) been articulated. The “anti-logical” penchant of multi-modal argumentation is not found at the object-level—in its countenancing “non-logical” modes of argument, but at the meta-level—in its resistance, as a mistaken embracing of the “logical” mode, to using the logics governing the different modes to self-regulate the course of our arguings. (shrink)

On Gilbert’s multi-modal theory of argumentation, the “logical” is but one among many modes of argument, including the emotional, the visceral (physical), and the kisceral (intuitive). Yet, I argue that, properly understood, the logical is not one mode among many. Rather, it is better understood as the _uber-mode_ of argument. What Gilbert calls the “logical mode” of argument—a linear, orderly, highly verbalizable, way of arguing—is made possible only to the extent that the logic of some space of reasons has (...) been articulated. The “anti-logical” penchant of multi-modal argumentation is not found at the object-level—in its countenancing “non-logical” modes of argument, but at the meta-level—in its resistance, as a mistaken embracing of the “logical” mode, to using the logics governing the different modes to self-regulate the course of our arguings. (shrink)

On Gilbert’s multi-modal theory of argumentation, the “logical” is but one among many modes of argument, including the emotional, the visceral (physical), and the kisceral (intuitive). Yet, I argue that, properly understood, the logical is not one mode among many. Rather, it is better understood as the _uber-mode_ of argument. What Gilbert calls the “logical mode” of argument—a linear, orderly, highly verbalizable, way of arguing—is made possible only to the extent that the logic of some space of reasons has (...) been articulated. The “anti-logical” penchant of multi-modal argumentation is not found at the object-level—in its countenancing “non-logical” modes of argument, but at the meta-level—in its resistance, as a mistaken embracing of the “logical” mode, to using the logics governing the different modes to self-regulate the course of our arguings. (shrink)

This book presents adaptive logics as an intuitive and powerful framework for modeling defeasible reasoning. It examines various contexts in which defeasible reasoning is useful and offers a compact introduction into adaptive logics. The author first familiarizes readers with defeasible reasoning, the adaptive logics framework, combinations of adaptive logics, and a range of useful meta-theoretic properties. He then offers a systematic study of adaptive logics based on various applications. The book presents formal models for defeasible (...) reasoning stemming from different contexts, such as default reasoning, argumentation, and normative reasoning. It highlights various meta-theoretic advantages of adaptive logics over other logics or logical frameworks that model defeasible reasoning. In this way the book substantiates the status of adaptive logics as a generic formal framework for defeasible reasoning. (shrink)

Short Arguments: Some General Rules Arguments begin by marshaling reasons and organizing them in a clear and fair way. Chapter I offers general rules for ...

In the most general terms, the Logical Connection Argument states that theory and practice are two inseparable aspects of the same thing. Every action, linguistic or otherwise, is an indivisible unity of content and the means by which it is expressed. Alternatively, we may talk of the inseparability of content and form, meaning and act of expression, goal and method or means of its realization, and so forth. The argument was meant to prove that intentions cannot be treated as causes (...) in social scientific explanation, but it did it at the cost of making any meta-analysis, and hence, critique, highly problematic. My position is that the LCA is indeed logical, and hence irrefutable. Nonetheless, we can distinguish between “raw” and “refined” versions of the argument. The refined version maintains that while ultimately and ideally, the content and means of expression presuppose one another in the sense that a content is inconceivable without a form, and vice versa, in reality there is never a perfect match between aims and methods. In typical circumstances, we do not have a precise sense of what we are doing; the meaning of our actions is gradually discovered in the course of exploratory behaviors, of which critique is an indispensable part. In this contribution, I venture to examine the problem from a neuropsychological perspective with the view to showing in exactly what sense and to what extent explorative behaviors and associated motivations preside over other activities. I argue that content is always underdetermined with respect to its form, and hence the alleged internal connection between them is not a given, but rather amounts to a regulative principle which motivates mutual adjustments. (shrink)

This paper introduces a multi-agent dynamic epistemic logic for abstract argumentation. Its main motivation is to build a general framework for modelling the dynamics of a debate, which entails reasoning about goals, beliefs, as well as policies of communication and information update by the participants. After locating our proposal and introducing the relevant tools from abstract argumentation, we proceed to build a three-tiered logical approach. At the first level, we use the language of propositional logic to encode states (...) of a multi-agent debate. This language allows to specify which arguments any agent is aware of, as well as their subjective justification status. We then extend our language and semantics to that of epistemic logic, in order to model individuals’ beliefs about the state of the debate, which includes uncertainty about the information available to others. As a third step, we introduce a framework of dynamic epistemic logic and its semantics, which is essentially based on so-called event models with factual change. We provide completeness results for a number of systems and show how existing formalisms for argumentation dynamics and unquantified uncertainty can be reduced to their semantics. The resulting framework allows reasoning about subtle epistemic and argumentative updates—such as the effects of different levels of trust in a source—and more in general about the epistemic dimensions of strategic communication. (shrink)

In this paper we examine Prior’s reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic K t 4 plus a new axiom ( P ): ‘ p Λ G p ⊃ P G p ’. This formula was used by Prior in his original analysis of Master Argument. ( P ) (...) is usually added as an extra axiom to an axiomatization of the logic of linear time. In that case the set of moments is a total order and must be left-discrete without the least moment. However, the logic of Master Argument does not require linear time. We show what properties of the set of moments are exactly forced by ( P ) in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction. (shrink)

This article investigates to what extent protocols for dynamicdisputes, i.e., disputes in which the information base can vary at differentstages, can be justified in terms of logics for defeasible argumentation. Firsta general framework is formulated for dialectical proof theories for suchlogics. Then this framework is adapted to serve as a framework for protocols fordynamic disputes, after which soundness and fairness properties are formulated for such protocols relative to dialectical proof theories. It then turns out that certaintypes of protocols (...) that are perfectly fine with a static information base, arenot sound or fair in a dynamic setting. Finally, a natural dynamic protocolis defined for which soundness and fairness can be established. (shrink)

Paperback. This volume finds its origin in a colloquium on Logic and Argumentation, held in June 1994 in Amsterdam and sponsored by the Royal Netherlands Academy of Arts and Sciences. The papers included have been selected for the role they can play in illuminating current thinking about the various kinds of relations between logic and argumentation.Aiming to provide some background to the academic endeavour of exploring the connections between logic and argumentation this volume offers the reader some (...) representative specimina of current thinking about this subject. (shrink)

_An enlightening introduction to the study of logic: its history, philosophical foundations, and formal structures_ _Logic: Inquiry, Argument, and Order_ is the first book of its kind to frame the study of introductory logic in terms of problems connected to wider issues of knowledge and judgment that arise in the context of racial, cultural, and religious diversity. With its accessible style and integration of philosophical inquiry and real-life concerns, this book offers a novel approach to the theory of logic and (...) its relevance to questions of meaning and value that arise in the world around us. The book poses four problems for logic: Is logic separate from experience? Does logic require dualisms? Can logic reconcile opposed ways of understanding the world? And when things are divided, does the boundary have a logic? The author begins the exploration of these questions with a discussion of the process of analyzing and constructing arguments. Using the logical theories of C. S. Peirce, John Dewey, and Josiah Royce to frame the investigation, subsequent chapters outline the process of inquiry, the concept of communicative action, the nature of validity, categorical reasoning through the theory of the syllogism, and inductive reasoning and probability. The book concludes with a presentation of modal logic, propositional logic, and quantification. Logic is presented as emerging from the activities of inquiry and communication, allowing readers to understand even the most difficult aspects of formal logic as straightforward developments of the process of anticipating and taking action. Numerous practice problems use arguments related to issues of diversity and social theory, and the book introduces methods of proving validity that include Venn diagrams, natural deduction, and the method of tableaux. _Logic: Inquiry, Argument, and Order_ is an ideal book for courses on philosophical methods and critical reasoning at the upper-undergraduate and graduate levels. It is also an insightful reference for anyone who would like to explore a cross-cultural approach to the topic of logic. (shrink)

In this paper we examine Prior's reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic $K_t 4$ plus a new axiom $:p \wedge Gp \supset PGp'$. This formula was used by Prior in his original analysis of Master Argument. is usually added as an extra axiom to an axiomatization of the (...) logic of linear time. In that case the set of moments is a total order and must be left-discrete without the least moment. However, the logic of Master Argument does not require linear time. We show what properties of the set of moments are exactly forced by in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction. (shrink)

This paper aims at laying some foundations of a logic of argumentation in which arguments, as well as attacks and supports among arguments are all defined in a unifying formalism. In the latter, an argument is denoted as a pair displaying a reason and a conclusion but no condition is required to hold relating the reason to the conclusion. We introduce a series of inference rules relating arguments and show how the resulting system captures important features of argumentation (...) that hitherto have not been captured by existing formalisms. (shrink)

The Handbook of the Logic of Argument and Inference is an authoritative reference work in a single volume, designed for the attention of senior undergraduates, graduate students and researchers in all the leading research areas concerned with the logic of practical argument and inference. After an introductory chapter, the role of standard logics is surveyed in two chapters. These chapters can serve as a mini-course for interested readers, in deductive and inductive logic, or as a refresher. Then follow two (...) chapters of criticism; one the internal critique and the other the empirical critique. The first deals with objections to standard logics (as theories of argument and inference) arising from the research programme in philosophical logic. The second canvasses criticisms arising from work in cognitive and experimental psychology. The next five chapters deal with developments in dialogue logic, interrogative logic, informal logic, probability logic and artificial intelligence. The last chapter surveys formal approaches to practical reasoning and anticipates possible future developments. Taken as a whole the Handbook is a single-volume indication of the present state of the logic of argument and inference at its conceptual and theoretical best. Future editions will periodically incorporate significant new developments. (shrink)

This paper briefly outlines some advancements in paraconsistent logics for modelling knowledge representation and reasoning. Emphasis is given on the so-called Logics of Formal Inconsistency (LFIs), a class of paraconsistent logics that formally internalize the very concept(s) of consistency and inconsistency. A couple of specialized systems based on the LFIs will be reviewed, including belief revision and probabilistic reasoning. Potential applications of those systems in the AI area of KRR are tackled by illustrating some examples that emphasizes (...) the importance of a fine-tuned treatment of consistency in modelling reputation systems, preferences, argumentation, and evidence. (shrink)

This is an introductory guide to the basic principles of constructing good arguments and criticizing bad ones. It is nontechnical in its approach, and is based on 150 key examples, each discussed and evaluated in clear, illustrative detail. The author explains how errors, fallacies, and other key failures of argument occur. He shows how correct uses of argument are based on sound argument strategies for reasoned persuasion and critical questions for responding. Among the many subjects covered are: techniques of posing, (...) replying to, and criticizing questions, forms of valid argument, relevance, appeals to emotion, personal attack, uses and abuses of expert opinion, problems in deploying statistics, loaded terms, equivocation, and arguments from analogy. (shrink)

As automation in artificial intelligence is increasing, we will need to automate a growing amount of ethical decision making. However, ethical decision- making raises novel challenges for engineers, ethicists and policymakers, who will have to explore new ways to realize this task. The presented work focuses on the development and formalization of models that aim at ensuring a correct ethical behaviour of artificial intelligent agents, in a provable way, extending and implementing a logic-based proving calculus that is based on (...) class='Hi'>argumentation reasoning with support and attack arguments. This leads to a formal theoretical framework of ethical competence that could be implemented in artificial intelligent systems in order to best formalize certain parameters of ethical decision-making to ensure safety and justified trust. (shrink)

Even though tools for identifying and analyzing arguments are now in wide use in the field of argumentation studies, so far there is a paucity of resources for evaluating real arguments, aside from using deductive logic or Bayesian rules that apply to inductive arguments. In this paper it is shown that recent developments in artificial intelligence in the area of computational systems for modeling defeasible argumentation reveal a different approach that is currently making interesting progress. It is shown (...) how these systems provide the general outlines for a system of argument evaluation that can be applied to legal arguments as well as everyday conversational arguments to assist a user to evaluate an argument. (shrink)

The virtues and vices of argument are now an established part of argumentation theory. They have helped direct attention to hitherto neglected aspects of how we argue. However, it remains controversial whether a virtue theory can contribute to some of the central questions of argumentation theory. Notably, Harvey Siegel disputes whether what he calls ‘arguments in the abstract propositional sense’ can be evaluated meaningfully within a virtue theory. This paper explores the prospects for grounding an account of argument (...) evaluation in arguers’ virtues and vices by examination of a corresponding debate in virtue ethics: Can an ethics of virtue guide our actions? It is thereby argued that an affirmative answer is possible: virtues suffice for argument evaluation. (shrink)

A key question in the philosophy of logic is how we have epistemic justification for claims about logical entailment (assuming we have such justification at all). Justification holism asserts that claims of logical entailment can only be justified in the context of an entire logical theory, e.g., classical, intuitionistic, paraconsistent, paracomplete etc. According to holism, claims of logical entailment cannot be atomistically justified as isolated statements, independently of theory choice. At present there is a developing interest in—and endorsement of—justification holism (...) due to the revival of an abductivist approach to the epistemology of logic. This paper presents an argument against holism by establishing a foundational entailment-sentence of deduction which is justified independently of theory choice and outside the context of a whole logical theory. (shrink)

This article investigates to what extent protocols for dynamicdisputes, i.e., disputes in which the information base can vary at differentstages, can be justified in terms of logics for defeasible argumentation. Firsta general framework is formulated for dialectical proof theories for suchlogics. Then this framework is adapted to serve as a framework for protocols fordynamic disputes, after which soundness and fairness properties are formulated for such protocols relative to dialectical proof theories. It then turns out that certaintypes of protocols (...) that are perfectly fine with a static information base, arenot sound or fair in a dynamic setting. Finally, a natural dynamic protocolis defined for which soundness and fairness can be established. (shrink)

The logical connection argument holds that factors which appear causally connected can be shown not to be so, At least when described in certain ways, If these factors are logically connected when so described. I argue that normal formulations of the logical connection argument confuse propositions and events. Moreover, When it is clarified in terms of "de re" necessity, It requires strong ontological assumptions for which no support is given and about the intelligibility of which there is reasonable question. I (...) conclude that the logical connection argument fails to give any reason for excluding any causal hypothesis. (shrink)

"A Workbook for Arguments" builds on Anthony Weston's "Rulebook for Arguments" to provide a complete textbook for a course in critical thinking or informal logic. "Workbook" includes: The entire text of "Rulebook," supplemented with extensive further explanations and exercises. Homework exercises adapted from a wide range of arguments from newspapers, philosophical texts, literature, movies, videos, and other sources. Practical advice to help students succeed when applying the "Rulebook's" rules to the examples in the homework exercises. Suggestions for further practice, outlining (...) activities that students can do by themselves or with classmates to improve their skills. Detailed instructions for in-class activities and take-home assignments designed to engage students. An appendix on mapping arguments, giving students a solid introduction to this vital skill in constructing complex and multi-step arguments and evaluating them. Model answers to odd-numbered problems, including commentaries on the strengths and weaknesses of selected sample answers and further discussion of some of the substantive intellectual, philosophical, or ethical issues they raise. (shrink)

The main currently unsolved problem in the theory of argumentation concerns the function of logic in argumentation and reasoning. The traditional view simply identified logic with the theory of reasoning. This view is still being echoed in older textbooks of formal logic. In a different variant, the same view is even codified in the ordinary usage of words such as ‘logic’, ‘deduction’, ‘inference’, etc. For each actual occurrence of these terms in textbooks of formal logic, there are hundreds (...) of uses of the same idioms to describe the feats of real or fictional detectives. I have called the idea reflected by this usage the “Sherlock Holmes conception of logic and deduction.” In the history of science, we find no less a thinker than Sir Isaac Newton describing his experimental method as one of analysis or resolution and claiming to have “deduced” at least some of his laws from the “phenomena.”. (shrink)

Classical logic yields counterintuitive results for numerous propositional argument forms. The usual alternatives (modal logic, relevance logic, etc.) generate counterintuitive results of their own. The counterintuitive results create problems—especially pedagogical problems—for informal logicians who wish to use formal logic to analyze ordinary argumentation. This paper presents a system, PL– (propositional logic minus the funny business), based on the idea that paradigmatic valid argument forms arise from justificatory or explanatory discourse. PL– avoids the pedagogical difficulties without sacrificing insight into argument.

This is an introductory guide to the basic principles of constructing good arguments and criticizing bad ones. It is nontechnical in its approach, and is based on 150 key examples, each discussed and evaluated in clear, illustrative detail. The author explains how errors, fallacies, and other key failures of argument occur. He shows how correct uses of argument are based on sound argument strategies for reasoned persuasion and critical questions for responding. Among the many subjects covered are: techniques of posing, (...) replying to, and criticizing questions, forms of valid argument, relevance, appeals to emotion, personal attack, uses and abuses of expert opinion, problems in deploying statistics, loaded terms, equivocation, and arguments from analogy. (shrink)

The need to distinguish between logical and extra-logical varieties of inference, entailment, validity, and consistency has played a prominent role in meta-ethical debates between expressivists and descriptivists. But, to date, the importance that matters of logical form play in these distinctions has been overlooked. That’s a mistake given the foundational place that logical form plays in our understanding of the difference between the logical and the extra-logical. This essay argues that descriptivists are better positioned than their expressivist rivals to provide (...) the needed account of logical form, and so better able to capture the needed distinctions. This finding is significant for several reasons: First, it provides a new argument against expressivism. Second, it reveals that descriptivists can make use of this new argument only if they are willing to take a controversial—but plausible—stand on claims about the nature and foundations of logic. (shrink)

"A Workbook for Arguments" builds on Anthony Weston’s "A Rulebook for Arguments" to provide a complete textbook for a course in critical thinking or informal logic. The second edition adds: Updated and improved homework exercises—nearly one third are new—to ensure that the examples continue to resonate with students. Increased coverage of scientific reasoning, demonstrating how scientific reasoning dovetails with critical thinking more generally Two new activities in which students analyze arguments in their original form, as provided in brief selections from (...) the original texts. This edition continues to include The entire text of "Rulebook," supplemented with extensive explanations and exercises. Homework exercises adapted from a wide range of arguments in a wide variety of sources. Practical advice to help students succeed. Model answers to odd-numbered problems, including commentaries on the strengths and weaknesses of selected sample answers and further discussion of some of the substantive intellectual, philosophical, or ethical issues they raise. Detailed instructions for in-class activities and take-home assignments. An appendix on mapping arguments, giving students a solid introduction to this vital skill in constructing complex and multi-step arguments and evaluating them. (shrink)

Some expressions of English, like the demonstratives ‘this’ and ‘that’, are referentially promiscuous: distinct free occurrences of them in the same sentence can differ in content relative to the same context. One lesson of referentially promiscuous expressions is that basic logical properties like validity and logical truth obtain or fail to obtain only relative to a context. This approach to logic can be developed in just as rigorous a manner as David Kaplan’s classic logic of demonstratives. The result is a (...) logic that applies to arguments in English containing multiple occurrences of referentially promiscuous expressions. (shrink)

In this paper I offer solutions to two problems which our moral practice engenders for expressivism, the meta-ethical doctrine according to which ethical statements aren't propositional, susceptible of truth and falsity, but, rather, express the speaker's non-cognitive attitudes. First, the expressivist must show that arguments which are valid when interpreted propositionally are valid when construed expressivistically, and vice versa. The second difficulty is the Frege-Geach problem. Moral arguments employ atomic sentences, negations, disjunctions, etc., and, by expressivist lights, the meaning of (...) a moral sentence depends on the attitude that it expresses. Since one's attitude varies as one asserts a claim, or negates it, or cites it as a disjunct, etc., the meaning of the relevant phrase changes as well, so the argument equivocates. (Formal proofs are provided in appendices to the paper.). (shrink)

Informal logic is a new sub-discipline of philosophy, roughly definable as the philosophy of argument. Contributors have challenged the traditional concept of an argument as a premiss-conclusion complex, in favour of speech-act, functional and dialogical conceptions; they have identified as additional components warrants, modal qualifiers, rebuttals, and a dialectical tier. They have objected that "soundness" is neither necessary nor sufficient for a good argument. Alternative proposals include acceptability, relevance and sufficiency of the premisses; conformity to a valid argument schema; conformity (...) to rules for discussion aimed at rational resolution of a dispute. Informal logic is a significant part of philosophy. (shrink)

In this article the argumentation structure of the court’s decision in the Popov v. Hayashi case is formalised in Prakken’s (Argument Comput 1:93–124; 2010) abstract framework for argument-based inference with structured arguments. In this framework, arguments are inference trees formed by applying two kinds of inference rules, strict and defeasible rules. Arguments can be attacked in three ways: attacking a premise, attacking a conclusion and attacking an inference. To resolve such conflicts, preferences may be used, which leads to three (...) corresponding kinds of defeat, after which Dung’s (Artif Intell 77:321–357; 1995) abstract acceptability semantics can be used to evaluate the arguments. In the present paper the abstract framework is instantiated with strict inference rules corresponding to first-order logic and with defeasible inference rules for defeasible modus ponens and various argument schemes. The main techniques used in the formal reconstruction of the case are rule-exception structures and arguments about rule validity. Arguments about socio-legal values and the use of precedent cases are reduced to arguments about rule validity. The tree structure of arguments, with explicit subargument relations between arguments, is used to capture the dependency relations between the elements of the court’s decision. (shrink)

This paper points out some problems with two recent logical systems – one due to Prakken and Sartor, the other due to Kowalski and Toni – designedfor the representation of defeasible arguments in general, but with a specialemphasis on legal reasoning.

This is just one typical example of a class of arguments which are sometimes used to attack those (such as the author of this article) who presume to criticise philosophers with different views, or from different cultures, by "dogmatically" appealing to the principles of logic. There is, as we shall see, something very odd about this sort of argument, but it does have a certain superficial plausibility, and also an air of moral virtue through its spirit of generous open-mindedness. Who (...) are we to criticise Plato, Descartes and the rest, for failing to live up to our limited Modern Western Logic? Our criticisms must be simply the result of narrow-minded bigotry, which prevents us from seeing that all standards are relative, and that the pretended "objectivity" of our logic is no more than a manifestation of our supreme cultural arrogance. (shrink)

Following a Toulmian account of argument analysis and evaluation, I offer a general unitary schema for, so called, deductive and inductive types of analogical arguments. This schema is able to explain why certain analogical arguments can be said to be deductive, and yet, also defeasible.

This paper compares the features and methods of the two leading implemented systems that offer a tool for helping a user to find or invent arguments to support or attack a designated conclusion, the Carneades Argumentation System and the IBM Watson Debater tool. The central aim is to contribute to the understanding of scholars in informal logic, rhetoric and argumentation on how these two software systems can be useful for them. One contribution of the paper is to explain (...) to these potential users how the two tools are applicable to the task of inventing arguments by using some simple illustrative examples. Another is to redefine the structure of argument invention as a procedure. (shrink)

This is an introductory guidebook to the basic principles of how to construct good arguments and how to criticeze bad ones. It is non-technical in its approach and is based on 150 key examples, each discussed and evaluated in clear, illustrative detail. Professor Walton, a leading authority in the field of informal logic, explains how errors, fallacies, and other key failures of argument occur. He shows how correct uses of argument are based on sound strategies for reasoned persuasion and critical (...) responses. Among the many subjects covered are: forms of valid argument, relevance, appeals to emotion, personal attack, uses and abuses of expert opinion, problems in deploying statistics, loading terms, equivocation, arguments from analogy, and techniques of posing, replying to, and criticizing questions. The book will be ideally suited to courses in informal logic and in the introduction to philosophy. It will also prove valuable to studetns of pragmatics, rhetoric, and speech communication. (shrink)

An abstract framework for structured arguments is presented, which instantiates Dung's ('On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming, and n- Person Games', Artificial Intelligence , 77, 321-357) abstract argumentation frameworks. Arguments are defined as inference trees formed by applying two kinds of inference rules: strict and defeasible rules. This naturally leads to three ways of attacking an argument: attacking a premise, attacking a conclusion and attacking an inference. To resolve such attacks, preferences (...) may be used, which leads to three corresponding kinds of defeat: undermining, rebutting and undercutting defeats. The nature of the inference rules, the structure of the logical language on which they operate and the origin of the preferences are, apart from some basic assumptions, left unspecified. The resulting framework integrates work of Pollock, Vreeswijk and others on the structure of arguments and the nature of defeat and extends it in several respects. Various rationality postulates are proved to be satisfied by the framework, and several existing approaches are proved to be a special case of the framework, including assumption-based argumentation and DefLog. (shrink)

In the School of Mathematical Sciences at Queen Mary in the University of London we have been running a module that teaches the students to write good mathematical English. The module is for second-year undergraduates and has been running for three years. It is based on logic, but the logic—though mathematically precise—is informal and doesn't use logical symbols. Some theory of definitions is taught in order to give a structure for mathematical descriptions, and some natural deduction rules form a basis (...) for writing mathematical arguments. Alongside this logical material, the students have weekly exercises that involve writing informal explanations of simple mathematical ideas for non-mathematicians. (shrink)

The present author developed a calculus for the logic of ‘because’. In a recent paper in this journal, it has been claimed that the central inference rules for the logic are invalid and that the intuition upon which the rules are based is not accounted for. This note criticises these arguments and presents an independent argument in favour of the rules used in the logic.

According to a very widespread interpretation of the metaphysical nature of quantum entities—the so-called Received View on quantum non-individuality—, quantum entities are non-individuals. Still according to this understanding, non-individuals are entities for which identity is restricted or else does not apply at all. As a consequence, it is said, such approach to quantum mechanics would require that classical logic be revised, given that it is somehow committed with the unrestricted validity of identity. In this paper we examine the arguments to (...) the inadequacy of classical logic to deal with non-individuals, as previously defined, and argue that they fail to make a good case for logical revision. In fact, classical logic may accommodate non-individuals in that specific sense too. What is more pressing for the Received View, it seems, is not a revision of logic, but rather a more adequate metaphysical characterization of non-individuals. (shrink)

The issue of a logic foundation for African thought connects well with the question of method. Do we need new methods for African philosophy and studies? Or, are the methods of Western thought adequate for African intellectual space? These questions are not some of the easiest to answer because they lead straight to the question of whether or not a logic tradition from African intellectual space is possible. Thus in charting the course of future direction in African philosophy and studies, (...) one must be confronted with this question of logic. The author boldly takes up this challenge and becomes the first to do so in a book by introducing new concepts and formulating a new African culture-inspired system of logic called Ezumezu which he believes would ground new methods in African philosophy and studies. He develops this system to rescue African philosophy and, by extension, sundry fields in African Indigenous Knowledge Systems from the spell of Plato and the hegemony of Aristotle. African philosophers can now ground their discourses in Ezumezu logic which will distinguish their philosophy as a tradition in its own right. On the whole, the book engages with some of the lingering controversies in the idea of African logic before unveiling Ezumezu as a philosophy of logic, methodology and formal system. The book also provides fresh arguments and insights on the themes of decolonisation and Africanisation for the intellectual transformation of scholarship in Africa. It will appeal to philosophers and logicians—undergraduates and post graduate researchers—as well as those in various areas of African studies. (shrink)

Answer-set programming (ASP) has emerged as a declarative programming paradigm where problems are encoded as logic programs, such that the so-called answer sets of theses programs represent the solutions of the encoded problem. The efficiency of the latest ASP solvers reached a state that makes them applicable for problems of practical importance. Consequently, problems from many different areas, including diagnosis, data integration, and graph theory, have been successfully tackled via ASP. In this work, we present such ASP-encodings for problems associated (...) to abstract argumentation frameworks (AFs) and generalisations thereof. Our encodings are formulated as fixed queries, such that the input is the only part depending on the actual AF to process. We illustrate the functioning of this approach, which is underlying a new argumentation system called ASPARTIX in detail and show its adequacy in terms of computational complexity. (shrink)