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The logic of argumentation (LA) is a formalised description of the ways in which humans reason and argue about propositions. It is used, for example, in computer artificial intelligence systems in the fields of medical diagnosis and prognosis, and research chemistry.
Krause et al. [1] appear to have been the first authors to use the term "logic of argumentation" in a paper about their model for using argumentation for qualitative reasoning under uncertainty, although the approach had been used earlier in prototype computer applications to support medical diagnosis. [2] [3] Their ideas have been developed further, [4] [5] and used in applications for predicting chemical toxicity and xenobiotic metabolism, for example. [6] [7]
In LA, arguments for and arguments against a proposition are distinct; an argument for a proposition contributes nothing to the case against it, and vice versa. Among other things, this means that LA can support contradiction – proof that an argument is true and that it is false. Arguments supporting the case for and arguments supporting the case against are aggregated separately, leading to a single assessment of confidence in the case for and a single assessment of confidence in the case against. Then the two are resolved to provide a single measure of confidence in the proposition.
In most implementations of LA the default aggregated value is equal to the strongest value in the set of arguments for or against the proposition. Having more than one argument in agreement does not automatically increase confidence because it cannot be assumed that the arguments are independent when reasoning under uncertainty. If there is evidence that arguments are independent and there is a case for increased confidence when they agree, this is sometimes expressed in additional rules of the form "If A and B then ...".
The process of aggregation and resolution can be represented as follows:
T = Resolve[Max{For(Ca,x, Cb,y, ...)}, Max{Against(Ca,x, Cb,y, ...)}]
where T is the overall assessment of confidence in a proposition; Resolve[] is a function which returns the single confidence value which is the resolution of any pair of values; For and Against are the sets of arguments supporting and opposing the proposition, respectively; Ca,x, Cb,y, ..., are the confidence values for those arguments; Max{...} is a function which returns the strongest member of the set upon which it operates (For or Against).
Arguments may assign confidence to propositions that themselves influence confidence in other arguments, and one rule may be undercut by another. A computer implementation can recognize these interrelationships to construct reasoning trees automatically.
The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory (DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories. First introduced by Arthur P. Dempster in the context of statistical inference, the theory was later developed by Glenn Shafer into a general framework for modeling epistemic uncertainty—a mathematical theory of evidence. The theory allows one to combine evidence from different sources and arrive at a degree of belief that takes into account all the available evidence.
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle. Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular evidence to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, contradistinguishing abduction from induction.
In classical logic, propositions are typically unambiguously considered as being true or false. For instance, the proposition one is both equal and not equal to itself is regarded as simply false, being contrary to the Law of Noncontradiction; while the proposition one is equal to one is regarded as simply true, by the Law of Identity. However, some mathematicians, computer scientists, and philosophers have been attracted to the idea that a proposition might be more or less true, rather than wholly true or wholly false. Consider My coffee is hot.
Default logic is a non-monotonic logic proposed by Raymond Reiter to formalize reasoning with default assumptions.
Argumentation theory is the interdisciplinary study of how conclusions can be supported or undermined by premises through logical reasoning. With historical origins in logic, dialectic, and rhetoric, argumentation theory includes the arts and sciences of civil debate, dialogue, conversation, and persuasion. It studies rules of inference, logic, and procedural rules in both artificial and real-world settings.
The expression computational intelligence (CI) usually refers to the ability of a computer to learn a specific task from data or experimental observation. Even though it is commonly considered a synonym of soft computing, there is still no commonly accepted definition of computational intelligence.
Legal informatics is an area within information science.
In philosophy of logic, defeasible reasoning is a kind of provisional reasoning that is rationally compelling, though not deductively valid. It usually occurs when a rule is given, but there may be specific exceptions to the rule, or subclasses that are subject to a different rule. Defeasibility is found in literatures that are concerned with argument and the process of argument, or heuristic reasoning.
Circumscription is a non-monotonic logic created by John McCarthy to formalize the common sense assumption that things are as expected unless otherwise specified. Circumscription was later used by McCarthy in an attempt to solve the frame problem. To implement circumscription in its initial formulation, McCarthy augmented first-order logic to allow the minimization of the extension of some predicates, where the extension of a predicate is the set of tuples of values the predicate is true on. This minimization is similar to the closed-world assumption that what is not known to be true is false.
In computer science, in particular in knowledge representation and reasoning and metalogic, the area of automated reasoning is dedicated to understanding different aspects of reasoning. The study of automated reasoning helps produce computer programs that allow computers to reason completely, or nearly completely, automatically. Although automated reasoning is considered a sub-field of artificial intelligence, it also has connections with theoretical computer science and philosophy.
Probabilistic logic involves the use of probability and logic to deal with uncertain situations. Probabilistic logic extends traditional logic truth tables with probabilistic expressions. A difficulty of probabilistic logics is their tendency to multiply the computational complexities of their probabilistic and logical components. Other difficulties include the possibility of counter-intuitive results, such as in case of belief fusion in Dempster–Shafer theory. Source trust and epistemic uncertainty about the probabilities they provide, such as defined in subjective logic, are additional elements to consider. The need to deal with a broad variety of contexts and issues has led to many different proposals.
Douglas Neil Walton was a Canadian academic and author, known for his books and papers on argumentation, logical fallacies and informal logic. He was a Distinguished Research Fellow of the Centre for Research in Reasoning, Argumentation, and Rhetoric (CRRAR) at the University of Windsor, Ontario, Canada, and before that (2008–2014), he held the Assumption Chair of Argumentation Studies at the University of Windsor. Walton's work has been used to better prepare legal arguments and to help develop artificial intelligence.
Subjective logic is a type of probabilistic logic that explicitly takes epistemic uncertainty and source trust into account. In general, subjective logic is suitable for modeling and analysing situations involving uncertainty and relatively unreliable sources. For example, it can be used for modeling and analysing trust networks and Bayesian networks.
An argument is a series of sentences, statements, or propositions some of which are called premises and one is the conclusion. The purpose of an argument is to give reasons for one's conclusion via justification, explanation, and/or persuasion.
Louis Hodes was an American mathematician, computer scientist, and cancer researcher.
In information technology a reasoning system is a software system that generates conclusions from available knowledge using logical techniques such as deduction and induction. Reasoning systems play an important role in the implementation of artificial intelligence and knowledge-based systems.
Trevor Bench-Capon is a British computer scientist and an Honorary Visiting Professor of computer science at the University of Liverpool, where he taught from 1987 until his retirement in 2012. He is the author of work on computer science and ontology and is one of the editors in chief of the Artificial Intelligence and Law Journal.
A legal expert system is a domain-specific expert system that uses artificial intelligence to emulate the decision-making abilities of a human expert in the field of law. Legal expert systems employ a rule base or knowledge base and an inference engine to accumulate, reference and produce expert knowledge on specific subjects within the legal domain.
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or logical truths. It studies how conclusions follow from premises due to the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. It examines arguments expressed in natural language while formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics.
This glossary of artificial intelligence is a list of definitions of terms and concepts relevant to the study of artificial intelligence, its sub-disciplines, and related fields. Related glossaries include Glossary of computer science, Glossary of robotics, and Glossary of machine vision.