4,228 research outputs found

    Interactive Learning-Based Realizability for Heyting Arithmetic with EM1

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    We apply to the semantics of Arithmetic the idea of ``finite approximation'' used to provide computational interpretations of Herbrand's Theorem, and we interpret classical proofs as constructive proofs (with constructive rules for ∨,∃\vee, \exists) over a suitable structure \StructureN for the language of natural numbers and maps of G\"odel's system \SystemT. We introduce a new Realizability semantics we call ``Interactive learning-based Realizability'', for Heyting Arithmetic plus \EM_1 (Excluded middle axiom restricted to Σ10\Sigma^0_1 formulas). Individuals of \StructureN evolve with time, and realizers may ``interact'' with them, by influencing their evolution. We build our semantics over Avigad's fixed point result, but the same semantics may be defined over different constructive interpretations of classical arithmetic (Berardi and de' Liguoro use continuations). Our notion of realizability extends intuitionistic realizability and differs from it only in the atomic case: we interpret atomic realizers as ``learning agents''

    Levels of discontinuity, limit-computability, and jump operators

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    We develop a general theory of jump operators, which is intended to provide an abstraction of the notion of "limit-computability" on represented spaces. Jump operators also provide a framework with a strong categorical flavor for investigating degrees of discontinuity of functions and hierarchies of sets on represented spaces. We will provide a thorough investigation within this framework of a hierarchy of Δ20\Delta^0_2-measurable functions between arbitrary countably based T0T_0-spaces, which captures the notion of computing with ordinal mind-change bounds. Our abstract approach not only raises new questions but also sheds new light on previous results. For example, we introduce a notion of "higher order" descriptive set theoretical objects, we generalize a recent characterization of the computability theoretic notion of "lowness" in terms of adjoint functors, and we show that our framework encompasses ordinal quantifications of the non-constructiveness of Hilbert's finite basis theorem

    Inductive Inference and Reverse Mathematics

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    The present work investigates inductive inference from the perspective of reverse mathematics. Reverse mathematics is a framework which relates the proof strength of theorems and axioms throughout many areas of mathematics in an interdisciplinary way. The present work looks at basic notions of learnability including Angluin\u27s tell-tale condition and its variants for learning in the limit and for conservative learning. Furthermore, the more general criterion of partial learning is investigated. These notions are studied in the reverse mathematics context for uniformly and weakly represented families of languages. The results are stated in terms of axioms referring to domination and induction strength

    Bayesian Inference Semantics: A Modelling System and A Test Suite

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    We present BIS, a Bayesian Inference Seman- tics, for probabilistic reasoning in natural lan- guage. The current system is based on the framework of Bernardy et al. (2018), but de- parts from it in important respects. BIS makes use of Bayesian learning for inferring a hy- pothesis from premises. This involves estimat- ing the probability of the hypothesis, given the data supplied by the premises of an argument. It uses a syntactic parser to generate typed syn- tactic structures that serve as input to a model generation system. Sentences are interpreted compositionally to probabilistic programs, and the corresponding truth values are estimated using sampling methods. BIS successfully deals with various probabilistic semantic phe- nomena, including frequency adverbs, gener- alised quantifiers, generics, and vague predi- cates. It performs well on a number of interest- ing probabilistic reasoning tasks. It also sus- tains most classically valid inferences (instan- tiation, de Morgan’s laws, etc.). To test BIS we have built an experimental test suite with examples of a range of probabilistic and clas- sical inference patterns

    A Systematic Literature Review of Digital Game-based Assessment Empirical Studies: Current Trends and Open Challenges

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    Technology has become an essential part of our everyday life, and its use in educational environments keeps growing. In addition, games are one of the most popular activities across cultures and ages, and there is ample evidence that supports the benefits of using games for assessment. This field is commonly known as game-based assessment (GBA), which refers to the use of games to assess learners' competencies, skills, or knowledge. This paper analyzes the current status of the GBA field by performing the first systematic literature review on empirical GBA studies, based on 66 research papers that used digital GBAs to determine: (1) the context where the study has been applied, (2) the primary purpose, (3) the knowledge domain of the game used, (4) game/tool availability, (5) the size of the data sample, (6) the data science techniques and algorithms applied, (7) the targeted stakeholders of the study, and (8) what limitations and challenges are reported by authors. Based on the categories established and our analysis, the findings suggest that GBAs are mainly used in formal education and for assessment purposes, and most GBAs focus on assessing STEM content and cognitive skills. Furthermore, the current limitations indicate that future GBA research would benefit from the use of bigger data samples and more specialized algorithms. Based on our results, we discuss the status of the field with the current trends and the open challenges (including replication and validation problems) providing recommendations for the future research agenda of the GBA field.Comment: 23 pages, 12 figures, 1 tabl

    Aspects of the constructive omega rule within automated deduction

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    In general, cut elimination holds for arithmetical systems with the w -rule, but not for systems with ordinary induction. Hence in the latter, there is the problem of generalisation, since arbitrary formulae can be cut in. This makes automatic theorem -proving very difficult. An important technique for investigating derivability in formal systems of arithmetic has been to embed such systems into semi- formal systems with the w -rule. This thesis describes the implementation of such a system. Moreover, an important application is presented in the form of a new method of generalisation by means of "guiding proofs" in the stronger system, which sometimes succeeds in producing proofs in the original system when other methods fail

    Decision tree learning for intelligent mobile robot navigation

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    The replication of human intelligence, learning and reasoning by means of computer algorithms is termed Artificial Intelligence (Al) and the interaction of such algorithms with the physical world can be achieved using robotics. The work described in this thesis investigates the applications of concept learning (an approach which takes its inspiration from biological motivations and from survival instincts in particular) to robot control and path planning. The methodology of concept learning has been applied using learning decision trees (DTs) which induce domain knowledge from a finite set of training vectors which in turn describe systematically a physical entity and are used to train a robot to learn new concepts and to adapt its behaviour. To achieve behaviour learning, this work introduces the novel approach of hierarchical learning and knowledge decomposition to the frame of the reactive robot architecture. Following the analogy with survival instincts, the robot is first taught how to survive in very simple and homogeneous environments, namely a world without any disturbances or any kind of "hostility". Once this simple behaviour, named a primitive, has been established, the robot is trained to adapt new knowledge to cope with increasingly complex environments by adding further worlds to its existing knowledge. The repertoire of the robot behaviours in the form of symbolic knowledge is retained in a hierarchy of clustered decision trees (DTs) accommodating a number of primitives. To classify robot perceptions, control rules are synthesised using symbolic knowledge derived from searching the hierarchy of DTs. A second novel concept is introduced, namely that of multi-dimensional fuzzy associative memories (MDFAMs). These are clustered fuzzy decision trees (FDTs) which are trained locally and accommodate specific perceptual knowledge. Fuzzy logic is incorporated to deal with inherent noise in sensory data and to merge conflicting behaviours of the DTs. In this thesis, the feasibility of the developed techniques is illustrated in the robot applications, their benefits and drawbacks are discussed
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