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  1. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games.Phan Minh Dung - 1995 - Artificial Intelligence 77 (2):321-357.
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  • An abstract framework for argumentation with structured arguments.Henry Prakken - 2010 - Argument and Computation 1 (2):93-124.
    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 (...)
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  • Reasoning with logical bilattices.Ofer Arieli & Arnon Avron - 1996 - Journal of Logic, Language and Information 5 (1):25--63.
    The notion of bilattice was introduced by Ginsberg, and further examined by Fitting, as a general framework for many applications. In the present paper we develop proof systems, which correspond to bilattices in an essential way. For this goal we introduce the notion of logical bilattices. We also show how they can be used for efficient inferences from possibly inconsistent data. For this we incorporate certain ideas of Kifer and Lozinskii, which happen to suit well the context of our work. (...)
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  • Reasoning about preferences in argumentation frameworks.Sanjay Modgil - 2009 - Artificial Intelligence 173 (9-10):901-934.
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  • SCC-recursiveness: a general schema for argumentation semantics.Pietro Baroni, Massimiliano Giacomin & Giovanni Guida - 2005 - Artificial Intelligence 168 (1-2):162-210.
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  • Fibring Argumentation Frames.Dov M. Gabbay - 2009 - Studia Logica 93 (2):231-295.
    This paper is part of a research program centered around argumentation networks and offering several research directions for argumentation networks, with a view of using such networks for integrating logics and network reasoning. In Section 1 we introduce our program manifesto. In Section 2 we motivate and show how to substitute one argumentation network as a node in another argumentation network. Substitution is a purely logical operation and doing it for networks, besides developing their theory further, also helps us see (...)
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  • Methods for solving reasoning problems in abstract argumentation – A survey.Günther Charwat, Wolfgang Dvořák, Sarah A. Gaggl, Johannes P. Wallner & Stefan Woltran - 2015 - Artificial Intelligence 220 (C):28-63.
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  • Equational approach to argumentation networks.D. M. Gabbay - 2012 - Argument and Computation 3 (2-3):87 - 142.
    This paper provides equational semantics for Dung's argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the ?extensions? of the network. This approach is very general and includes the Caminada labelling as a special case, as well as many other so-called network extensions, support systems, higher level attacks, Boolean networks, dependence on time, and much more. The equational approach has its conceptual roots in the nineteenth (...)
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  • Semantics for Higher Level Attacks in Extended Argumentation Frames Part 1: Overview.Dov M. Gabbay - 2009 - Studia Logica 93 (2-3):357-381.
    In 2005 the author introduced networks which allow attacks on attacks of any level. So if a → b reads a attacks 6, then this attack can itself be attacked by another node c. This attack itself can attack another node d. This situation can be iterated to any level with attacks and nodes attacking other attacks and other nodes. In this paper we provide semantics to such networks. We offer three different approaches to obtaining semantics. 1. The translation approach (...)
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  • A QBF-based formalization of abstract argumentation semantics.Ofer Arieli & Martin W. A. Caminada - 2013 - Journal of Applied Logic 11 (2):229-252.
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  • Temporal, numerical and meta-level dynamics in argumentation networks.H. Barringer, D. M. Gabbay & J. Woods - 2012 - Argument and Computation 3 (2-3):143-202.
    This paper studies general numerical networks with support and attack. Our starting point is argumentation networks with the Caminada labelling of three values 1=in, 0=out and ½=undecided. This is generalised to arbitrary values in [01], which enables us to compare with other numerical networks such as predator?prey ecological networks, flow networks, logical modal networks and more. This new point of view allows us to see the place of argumentation networks in the overall landscape of networks and import and export ideas (...)
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  • Theory of disjunctive attacks, Part I.D. Gabbay & M. Gabbay - 2016 - Logic Journal of the IGPL 24 (2):186-218.
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  • Argumentation: Reasoning Universalis.Antonis Kakas - 2022 - Studia Humana 11 (3-4):6-17.
    Can argumentation form the basis for any form of reasoning, informal or formal logical reasoning? We examine this question from the particular perspective of the recent developments in logic-based Artificial Intelligence (AI). We propose that argumentation provides the wider framework encompassing uniformly all reasoning, with strict or formal logical reasoning being a special boundary case. We also attempt to link this unifying role of argumentation with Aristotle’s original investigation of methods and forrmalisms for the systematic study of human reasoning.
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  • Comments On The Logic Of Constructible Falsity.Allen Hazen - 1980 - Bulletin of the Section of Logic 9 (1):10-13.
    Nelson has presented a constructive arithmetic with a negation opera- tion () dierent from the ordinary intuitionistic one . In [5] he presents a variant of Kleene's realization semantics for intuitionistic arithmetic, and proves that relative to this interpretation the arithmetic language with { has the same expressive power as the usual intuitionistic one, and fact certain theories of arithmetic incorporating his negation are equivalent to corresponding systems of intuitionistic arithmetic. A Fitch style natural deduction formulation ) of the pure (...)
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