65 research outputs found

    Ranking Theory

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    Ranking theory is one of the salient formal representations of doxastic states. It differs from others in being able to represent belief in a proposition (= taking it to be true), to also represent degrees of belief (i.e. beliefs as more or less firm), and thus to generally account for the dynamics of these beliefs. It does so on the basis of fundamental and compelling rationality postulates and is hence one way of explicating the rational structure of doxastic states. Thereby it provides foundations for accounts of defeasible or nonmonotonic reasoning. It has widespread applications in philosophy, it proves to be most useful in Artificial Intelligence, and it has started to find applications as a model of reasoning in psychology

    Online Handbook of Argumentation for AI: Volume 1

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    This volume contains revised versions of the papers selected for the first volume of the Online Handbook of Argumentation for AI (OHAAI). Previously, formal theories of argument and argument interaction have been proposed and studied, and this has led to the more recent study of computational models of argument. Argumentation, as a field within artificial intelligence (AI), is highly relevant for researchers interested in symbolic representations of knowledge and defeasible reasoning. The purpose of this handbook is to provide an open access and curated anthology for the argumentation research community. OHAAI is designed to serve as a research hub to keep track of the latest and upcoming PhD-driven research on the theory and application of argumentation in all areas related to AI.Comment: editor: Federico Castagna and Francesca Mosca and Jack Mumford and Stefan Sarkadi and Andreas Xydi

    What Should Default Reasoning be, by Default?

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    Author index—Volumes 1–89

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    A predicated network formalism for commonsense reasoning.

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    Chiu, Yiu Man Edmund.Thesis submitted in: December 1999.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 269-248).Abstracts in English and Chinese.Abstract --- p.iAcknowledgments --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- The Beginning Story --- p.2Chapter 1.2 --- Background --- p.3Chapter 1.2.1 --- History of Nonmonotonic Reasoning --- p.3Chapter 1.2.2 --- Formalizations of Nonmonotonic Reasoning --- p.6Chapter 1.2.3 --- Belief Revision --- p.13Chapter 1.2.4 --- Network Representation of Knowledge --- p.17Chapter 1.2.5 --- Reference from Logic Programming --- p.21Chapter 1.2.6 --- Recent Work on Network-type Automatic Reasoning Sys- tems --- p.22Chapter 1.3 --- A Novel Inference Network Approach --- p.23Chapter 1.4 --- Objectives --- p.23Chapter 1.5 --- Organization of the Thesis --- p.24Chapter 2 --- The Predicate Inference Network PIN --- p.25Chapter 2.1 --- Preliminary Terms --- p.26Chapter 2.2 --- Overall Structure --- p.27Chapter 2.3 --- Object Layer --- p.29Chapter 2.3.1 --- Virtual Object --- p.31Chapter 2.4 --- Predicate Layer --- p.33Chapter 2.4.1 --- Node Values --- p.34Chapter 2.4.2 --- Information Source --- p.35Chapter 2.4.3 --- Belief State --- p.36Chapter 2.4.4 --- Predicates --- p.37Chapter 2.4.5 --- Prototypical Predicates --- p.37Chapter 2.4.6 --- Multiple Inputs for a Single Belief --- p.39Chapter 2.4.7 --- External Program Call --- p.39Chapter 2.5 --- Variable Layer --- p.40Chapter 2.6 --- Inter-Layer Links --- p.42Chapter 2.7 --- Chapter Summary --- p.43Chapter 3 --- Computation for PIN --- p.44Chapter 3.1 --- Computation Functions for Propagation --- p.45Chapter 3.1.1 --- Computational Functions for Combinative Links --- p.45Chapter 3.1.2 --- Computational Functions for Alternative Links --- p.49Chapter 3.2 --- Applying the Computation Functions --- p.52Chapter 3.3 --- Relations Represented in PIN --- p.55Chapter 3.3.1 --- Relations Represented by Combinative Links --- p.56Chapter 3.3.2 --- Relations Represented by Alternative Links --- p.59Chapter 3.4 --- Chapter Summary --- p.61Chapter 4 --- Dynamic Knowledge Update --- p.62Chapter 4.1 --- Operations for Knowledge Update --- p.63Chapter 4.2 --- Logical Expression --- p.63Chapter 4.3 --- Applicability of Operators --- p.64Chapter 4.4 --- Add Operation --- p.65Chapter 4.4.1 --- Add a fully instantiated single predicate proposition with no virtual object --- p.66Chapter 4.4.2 --- Add a fully instantiated pure disjunction --- p.68Chapter 4.4.3 --- Add a fully instantiated expression which is a conjunction --- p.71Chapter 4.4.4 --- Add a human biased relation --- p.74Chapter 4.4.5 --- Add a single predicate expression with virtual objects --- p.76Chapter 4.4.6 --- Add a IF-THEN rule --- p.80Chapter 4.5 --- Remove Operation --- p.88Chapter 4.5.1 --- Remove a Belief --- p.88Chapter 4.5.2 --- Remove a Rule --- p.91Chapter 4.6 --- Revise Operation --- p.94Chapter 4.6.1 --- Revise a Belief --- p.94Chapter 4.6.2 --- Revise a Rule --- p.96Chapter 4.7 --- Consistency Maintenance --- p.97Chapter 4.7.1 --- Logical Suppression --- p.98Chapter 4.7.2 --- Example on Handling Inconsistent Information --- p.99Chapter 4.8 --- Chapter Summary --- p.102Chapter 5 --- Knowledge Query --- p.103Chapter 5.1 --- Domains of Quantification --- p.104Chapter 5.2 --- Reasoning through Recursive Rules --- p.109Chapter 5.2.1 --- Infinite Looping Control --- p.110Chapter 5.2.2 --- Proof of the finite termination of recursive rules --- p.111Chapter 5.3 --- Query Functions --- p.117Chapter 5.4 --- Type I Queries --- p.119Chapter 5.4.1 --- Querying a Simple Single Predicate Proposition (Type I) --- p.122Chapter 5.4.2 --- Querying a Belief with Logical Connective(s) (Type I) --- p.128Chapter 5.5 --- Type II Queries --- p.132Chapter 5.5.1 --- Querying Single Predicate Expressions (Type II) --- p.134Chapter 5.5.2 --- Querying an Expression with Logical Connectives (Type II) --- p.143Chapter 5.6 --- Querying an Expression with Virtual Objects --- p.152Chapter 5.6.1 --- Type I Queries Involving Virtual Object --- p.152Chapter 5.6.2 --- Type II Queries involving Virtual Objects --- p.156Chapter 5.7 --- Chapter Summary --- p.157Chapter 6 --- Uniqueness and Finite Termination --- p.159Chapter 6.1 --- Proof Structure --- p.160Chapter 6.2 --- Proof for Completeness and Finite Termination of Domain Search- ing Procedure --- p.161Chapter 6.3 --- Proofs for Type I Queries --- p.167Chapter 6.3.1 --- Proof for Single Predicate Expressions --- p.167Chapter 6.3.2 --- Proof of Type I Queries on Expressions with Logical Con- nectives --- p.172Chapter 6.3.3 --- General Proof for Type I Queries --- p.174Chapter 6.4 --- Proofs for Type II Queries --- p.175Chapter 6.4.1 --- Proof for Type II Queries on Single Predicate Expressions --- p.176Chapter 6.4.2 --- Proof for Type II Queries on Disjunctions --- p.178Chapter 6.4.3 --- Proof for Type II Queries on Conjunctions --- p.179Chapter 6.4.4 --- General Proof for Type II Queries --- p.181Chapter 6.5 --- Proof for Queries Involving Virtual Objects --- p.182Chapter 6.6 --- Uniqueness and Finite Termination of PIN Queries --- p.183Chapter 6.7 --- Chapter Summary --- p.184Chapter 7 --- Lifschitz's Benchmark Problems --- p.185Chapter 7.1 --- Structure --- p.186Chapter 7.2 --- Default Reasoning --- p.186Chapter 7.2.1 --- Basic Default Reasoning --- p.186Chapter 7.2.2 --- Default Reasoning with Irrelevant Information --- p.187Chapter 7.2.3 --- Default Reasoning with Several Defaults --- p.188Chapter 7.2.4 --- Default Reasoning with a Disabled Default --- p.190Chapter 7.2.5 --- Default Reasoning in Open Domain --- p.191Chapter 7.2.6 --- Reasoning about Unknown Exceptions I --- p.193Chapter 7.2.7 --- Reasoning about Unknown Exceptions II --- p.194Chapter 7.2.8 --- Reasoning about Unknown Exceptions III --- p.196Chapter 7.2.9 --- Priorities between Defaults --- p.198Chapter 7.2.10 --- Priorities between Instances of a Default --- p.199Chapter 7.2.11 --- Reasoning about Priorities --- p.199Chapter 7.3 --- Inheritance --- p.200Chapter 7.3.1 --- Linear Inheritance --- p.200Chapter 7.3.2 --- Tree-Structured Inheritance --- p.202Chapter 7.3.3 --- One-Step Multiple Inheritance --- p.203Chapter 7.3.4 --- Multiple Inheritance --- p.204Chapter 7.4 --- Uniqueness of Names --- p.205Chapter 7.4.1 --- Unique Names Hypothesis for Objects --- p.205Chapter 7.4.2 --- Unique Names Hypothesis for Functions --- p.206Chapter 7.5 --- Reasoning about Action --- p.206Chapter 7.6 --- Autoepistemic Reasoning --- p.206Chapter 7.6.1 --- Basic Autoepistemic Reasoning --- p.206Chapter 7.6.2 --- Autoepistemic Reasoning with Incomplete Information --- p.207Chapter 7.6.3 --- Autoepistemic Reasoning with Open Domain --- p.207Chapter 7.6.4 --- Autoepistemic Default Reasoning --- p.208Chapter 8 --- Comparison with PROLOG --- p.214Chapter 8.1 --- Introduction of PROLOG --- p.215Chapter 8.1.1 --- Brief History --- p.215Chapter 8.1.2 --- Structure and Inference --- p.215Chapter 8.1.3 --- Why Compare PIN with Prolog --- p.216Chapter 8.2 --- Representation Power --- p.216Chapter 8.2.1 --- Close World Assumption and Negation as Failure --- p.216Chapter 8.2.2 --- Horn Clauses --- p.217Chapter 8.2.3 --- Quantification --- p.218Chapter 8.2.4 --- Build-in Functions --- p.219Chapter 8.2.5 --- Other Representation Issues --- p.220Chapter 8.3 --- Inference and Query Processing --- p.220Chapter 8.3.1 --- Unification --- p.221Chapter 8.3.2 --- Resolution --- p.222Chapter 8.3.3 --- Computation Efficiency --- p.225Chapter 8.4 --- Knowledge Updating and Consistency Issues --- p.227Chapter 8.4.1 --- PIN and AGM Logic --- p.228Chapter 8.4.2 --- Knowledge Merging --- p.229Chapter 8.5 --- Chapter Summary --- p.229Chapter 9 --- Conclusion and Discussion --- p.230Chapter 9.1 --- Conclusion --- p.231Chapter 9.1.1 --- General Structure --- p.231Chapter 9.1.2 --- Representation Power --- p.231Chapter 9.1.3 --- Inference --- p.232Chapter 9.1.4 --- Dynamic Update and Consistency --- p.233Chapter 9.1.5 --- Soundness and Completeness Versus Efficiency --- p.233Chapter 9.2 --- Discussion --- p.234Chapter 9.2.1 --- Different Selection Criteria --- p.234Chapter 9.2.2 --- Link Order --- p.235Chapter 9.2.3 --- Inheritance Reasoning --- p.236Chapter 9.3 --- Future Work --- p.237Chapter 9.3.1 --- Implementation --- p.237Chapter 9.3.2 --- Application --- p.237Chapter 9.3.3 --- Probabilistic and Fuzzy PIN --- p.238Chapter 9.3.4 --- Temporal Reasoning --- p.238Bibliography --- p.23

    Modelling causal reasoning

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    PhDAlthough human causal reasoning is widely acknowledged as an object of scientific enquiry, there is little consensus on an appropriate measure of progress. Up-to-date evidence of the standard method of research in the field shows that this method has been rejected at the birth of modern science. We describe an instance of the standard scientific method for modelling causal reasoning (causal calculators). The method allows for uniform proofs of three relevant computational properties: correctness of the model with respect to the intended model, full abstraction of the model (function) with respect to the equivalence of reasoning scenarios (input), and formal relations of equivalence and subsumption between models. The method extends and exploits the systematic paradigm [Handbook of Logic in Artificial Intelligence and Logic Programming, volume IV, p. 439-498, Oxford 1995] to fit with our interpretation of it. Using the described method, we present results for some major models, with an updated summary spanning seventy-two years of research in the field

    Investigations in Belnap's Logic of Inconsistent and Unknown Information

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    Nuel Belnap schlug 1977 eine vierwertige Logik vor, die -- im Gegensatz zur klassischen Logik -- die Faehigkeit haben sollte, sowohl mit widerspruechlicher als auch mit fehlender Information umzugehen. Diese Logik hat jedoch den Nachteil, dass sie Saetze der Form 'wenn ..., dann ...' nicht ausdruecken kann. Ausgehend von dieser Beobachtung analysieren wir die beiden nichtklassischen Aspekte, Widerspruechlichkeit und fehlende Information, indem wir eine dreiwertige Logik entwickeln, die mit widerspruechlicher Information umgehen kann und eine Modallogik, die mit fehlender Information umgehen kann. Beide Logiken sind nicht monoton. Wir untersuchen Eigenschaften, wie z.B. Kompaktheit, Entscheidbarkeit, Deduktionstheoreme und Berechnungkomplexitaet dieser Logiken. Es stellt sich heraus, dass die dreiwertige Logik, nicht kompakt und ihre Folgerungsmenge im Allgemeinen nicht rekursiv aufzaehlbar ist. Beschraenkt man sich hingegen auf endliche Formelmengen, so ist die Folgerungsmenge rekursiv entscheidbar, liegt in der Klasse Σ2P\Sigma_2^P der polynomiellen Zeithierarchie und ist DIFFP-schwer. Wir geben ein auf semantischen Tableaux basierendes, korrektes und vollstaendiges Berechnungsverfahren fuer endliche Praemissenmengen an. Darueberhinaus untersuchen wir Abschwaechungen der Kompaktheitseigenschaft. Die nichtmonotone auf S5-Modellen basierende Modallogik stellt sich als nicht minder komplex heraus. Auch hier untersuchen wir eine sinnvolle Abschwaechung der Kompaktheitseigenschaft. Desweiteren studieren wir den Zusammenhang zu anderen nichtmonotonen Modallogiken wie Moores autoepistemischer Logik (AEL) und McDermotts NML-2. Wir zeigen, dass unsere Logik zwischen AEL und NML-2 liegt. Schliesslich koppeln wir die entworfene Modallogik mit der dreiwertigen Logik. Die dabei enstehende Logik MKT ist eine Erweiterung des nichtmonotonen Fragments von Belnaps Logik. Wir schliessen unsere Betrachtungen mit einem Vergleich von MKT und verschiedenen informationstheoretischen Logiken, wie z.B. Nelsons N und Heytings intuitionistischer Logik ab

    Logika, forma a argument

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    The goal of this thesis is to defend and explain the claim that traditional logical analysis is not the best tool for studying natural language argumentation. The most common critique directed at employment of logical formalisms as tools for analysis of the natural language is usually based on pointing out of differences between structure and semantics of natural languages and languages of logical formalisms. This is not the main issue, I believe. According to my findings the most fundamental problem of the traditional analysis is that it is based on many problematic epistemological assumptions, which are inherited from empiricist-positivist tradition. Namely the positivist version of the classical model of rationality as deductive reasoning from some basis of immediately verifiable and therefore unquestionable knowledge. The doctrine that every reasonable argumentation is reducible on deductions of such kinds is supposed to justify the traditional analysis of argumentation. My original contribution is mainly in showing that without abandoning those presuppositions, we cannot hope to arrive at better understanding of natural language argumentation by developing new and more precise logical formalisms. Logical formalisms are mere tools, which we have to use for the right purpose in the first place....Cílem mé disertace je obhájit a vysvětlit tezi, že tradiční logická analýza není vhodným nástrojem ke zkoumání argumentace v přirozeném jazyce. Nejčastější kritika formální logiky jako nástroje pro analýzu přirozeného jazyka je obvykle založena na poukázování na podstatné rozdíly mezi strukturou a sémantikou jazyků přirozených a jazyků logických formalismů. V tom však nevidím hlavní zdroj problémů. Podle mého úsudku je daleko zásadnějším problémem, že tradiční logická analýza často vychází z problematických epistemologických předpokladů, které analytická filosife zdědila z empiristicko- positivistické tradice. Jedná se především o pozitivistickou verzi klasického modelu racionality, jako deduktivního usuzování z nějaké báze bezprostředně ověřitelných a nepochybných poznatků. Přesvědčení, že každou rozumnou argumentaci lze redukovat na dedukci takového druhu je tím, co má ospravedlnit tradiční logickou analýzu. Můj přínos spočívá především v prokázání toho, že nezměníme-li zásadně tato východiska, pak nám pranic nepomůže, budeme-li zkoušet argumentaci v přirozeném jazyce analyzovat pomocí nových a přesnějších logických formaismů. Problém tedy není ani tak v samotném nástroji, jako spíše ve způsobu jeho užití. Pokud dostatečně zreflektujeme roli demonstrativního usuzování pro argumentaci jako...Department of LogicKatedra logikyFilozofická fakultaFaculty of Art
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