11 research outputs found

    Usuzování s nekonzistentními informacemi

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    Tato dizertační práce studuje extenze čtyřhodnotové Belnapovy-Dunnovy logiky, tzv. superbelnapovské logiky, z pohledu abstraktní algebraické logiky. Popisujeme v ní globální strukturu svazu superbelnapovských logik a ukazu- jeme, že tento svaz lze zcela popsat pomocí tříd konečných grafů splňujících jisté uzávěrové podmínky. Také zde zavádíme teorii tzv. explozivních extenzí a používáme ji k důkazu nových vět o úplnosti pro superbelnapovské logiky. Poté rozvíjeme gentzenovskou teorii důkazů pro tyto logiky a použijeme ji k důkazu věty o interpolaci pro mnoho z těchto logik. Nakonec také studujeme rozšíření Belnapovy-Dunnovy logiky o operátor pravdivosti ∆. Klíčová slova: abstraktní algebraická logika, Belnapova-Dunnova logika, parakonzistentní logika, superbelnapovské logikyThis thesis studies the extensions of the four-valued Belnap-Dunn logic, called super-Belnap logics, from the point of view of abstract algebraic logic. We describe the global structure of the lattice of super-Belnap logics and show that this lattice can be fully described in terms of classes of finite graphs satisfying some closure conditions. We also introduce a theory of so- called explosive extensions and use it to prove new completeness theorems for super-Belnap logics. A Gentzen-style proof theory for these logics is then developed and used to establish interpolation for many of them. Finally, we also study the expansion of the Belnap-Dunn logic by the truth operator ∆. Keywords: abstract algebraic logic, Belnap-Dunn logic, paraconsistent logic, super-Belnap logicsKatedra logikyDepartment of LogicFaculty of ArtsFilozofická fakult

    Automated Reasoning

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    This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

    Monoidal-Closed Categories of Tree Automata

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    We propose a realizability semantics for automata on infinite trees, based on categories of games built on usual simple games, and generalizing usual acceptance games of tree automata. Our approach can be summarized with the slogan " automata as objects, strategies as morphisms ". We show that the operations on tree automata used in the translations of MSO-formulae to automata (underlying Rabin's Theorem, that is the decidability of MSO on infinite trees) can be organized in a deduction system based on the multiplica-tive fragment of intuitionistic linear logic (ILL). Namely, we equip a variant of usual alternating tree automata (that we call uniform tree automata) with a fi-bred monoidal closed structure which in particular, via game determinacy handles a linear complementation of alternating automata, as well as deduction rules for exis-tential and universal quantifications. This monoidal structure is actually Cartesian on non-deterministic automata. Moreover, an adaptation of a usual construction for the simulation of alternating automata by non-deterministic ones satisfies the deduction rules of the !(−) ILL-exponential modality. Our realizability semantics satisfies an expected property of witness extraction from proofs of existential statements. Moreover, it allows to combine realizers produced as interpretations of proofs with strategies witnessing (non-)emptiness of tree automata, possibly obtained using external algorithms

    Fuzzy set covering as a new paradigm for the induction of fuzzy classification rules

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    In 1965 Lofti A. Zadeh proposed fuzzy sets as a generalization of crisp (or classic) sets to address the incapability of crisp sets to model uncertainty and vagueness inherent in the real world. Initially, fuzzy sets did not receive a very warm welcome as many academics stood skeptical towards a theory of imprecise'' mathematics. In the middle to late 1980's the success of fuzzy controllers brought fuzzy sets into the limelight, and many applications using fuzzy sets started appearing. In the early 1970's the first machine learning algorithms started appearing. The AQ family of algorithms pioneered by Ryszard S. Michalski is a good example of the family of set covering algorithms. This class of learning algorithm induces concept descriptions by a greedy construction of rules that describe (or cover) positive training examples but not negative training examples. The learning process is iterative, and in each iteration one rule is induced and the positive examples covered by the rule removed from the set of positive training examples. Because positive instances are separated from negative instances, the term separate-and-conquer has been used to contrast the learning strategy against decision tree induction that use a divide-and-conquer learning strategy. This dissertation proposes fuzzy set covering as a powerful rule induction strategy. We survey existing fuzzy learning algorithms, and conclude that very few fuzzy learning algorithms follow a greedy rule construction strategy and no publications to date made the link between fuzzy sets and set covering explicit. We first develop the theoretical aspects of fuzzy set covering, and then apply these in proposing the first fuzzy learning algorithm that apply set covering and make explicit use of a partial order for fuzzy classification rule induction. We also investigate several strategies to improve upon the basic algorithm, such as better search heuristics and different rule evaluation metrics. We then continue by proposing a general unifying framework for fuzzy set covering algorithms. We demonstrate the benefits of the framework and propose several further fuzzy set covering algorithms that fit within the framework. We compare fuzzy and crisp rule induction, and provide arguments in favour of fuzzy set covering as a rule induction strategy. We also show that our learning algorithms outperform other fuzzy rule learners on real world data. We further explore the idea of simultaneous concept learning in the fuzzy case, and continue to propose the first fuzzy decision list induction algorithm. Finally, we propose a first strategy for encoding the rule sets generated by our fuzzy set covering algorithms inside an equivalent neural network

    Search and planning under incomplete information : a study using Bridge card play

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    This thesis investigates problem-solving in domains featuring incomplete information and multiple agents with opposing goals. In particular, we describe Finesse --- a system that forms plans for the problem of declarer play in the game of Bridge. We begin by examining the problem of search. We formalise a best defence model of incomplete information games in which equilibrium point strategies can be identified, and identify two specific problems that can affect algorithms in such domains. In Bridge, we show that the best defence model corresponds to the typical model analysed in expert texts, and examine search algorithms which overcome the problems we have identified. Next, we look at how planning algorithms can be made to cope with the difficulties of such domains. This calls for the development of new techniques for representing uncertainty and actions with disjunctive effects, for coping with an opposition, and for reasoning about compound actions. We tackle these problems with a..

    Space programs summary no. 37-32, volume iv, for the period 1 february - 31 march 1965. supporting research and advanced development

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    Space programs on telecommunications, space science, propulsion, engineer mechanics, guidance and control, systems, and project engineerin

    The 1989 Goddard Conference on Space Applications of Artificial Intelligence

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    The following topics are addressed: mission operations support; planning and scheduling; fault isolation/diagnosis; image processing and machine vision; data management; and modeling and simulation
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