4,228 research outputs found
Interactive Learning-Based Realizability for Heyting Arithmetic with EM1
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
) 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
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
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 -measurable functions between arbitrary
countably based -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
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
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
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
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
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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