66,125 research outputs found
Inductive Inference with Additional Information
AbstractWe consider the problem of inductively inferring a grammar for a language, given (positive) examples of the language and putative (possibly faulty) grammars for the complement of the language. The criterion of success is identification in the limit, defined by E. M. Gold (1967, Inform. and Control10, 447–474). Additional information is useful insofar as it allows the identification of language classes that would not be identified with positive examples alone. An infinite sequence of grammars past some finite position are correct for the complement of the input language, is not as useful a form of additional information as a single correct grammar for the complement. Grammars that are almost correct for the complement (that is, that make finitely many errors) are not as useful as correct grammars, and the usefulness of a grammar decreases with increasing numbers of errors
Identification Critical Thinking Stages Of Students’ Mathematics Education Study Program FMIPA UNNES For Solving Mathematics Problems
This research is qualitative research that purpose to describe critical thinking stages of college students for each level of critical thinking skills in Mathematics Education Study Program FMIPA UNNES for solving mathematics problems. In the clarification, a subject in critical thinking level 0 until level 3 showed the same characteristic that is getting the information in the picture, and be able to create images to get additional information. In the assessment, subjects in critical thinking level 0 just dig a small portion of relevant information, the subject in critical thinking level 1 until level 3 dig most of the information. In the inference stage, a subject in critical thinking level 0 to level 2 only using inductive thinking, subject in critical thinking level 3 using deductive thinking. In the strategy stage, a subject in critical thinking 0 using the analogy or not can come up with strategies employed, subject in critical thinking level 1 and level 2 using the analogy, subject level 3 using his own ideas by looking for relationships in solving problems.
Keywords: critical thinking, the stages of critical thinking, clarification, assessment, inference, strategies , and solving mathematics problem
A comparative analysis of the effects of teaching writing in a foreign language with the application of the deductive and the inductive approach
The aim of this paper is to present and analyse the results of the study which focused on measuring the effectiveness of the deductive and inductive approach in teaching writing in a foreign language. The aim will be achieved through the introduction of a relevant theoretical background, the presentation of the research design, a brief description of the research and finally the presentation and analysis of the outcomes
A Bi-Directional Refinement Algorithm for the Calculus of (Co)Inductive Constructions
The paper describes the refinement algorithm for the Calculus of
(Co)Inductive Constructions (CIC) implemented in the interactive theorem prover
Matita. The refinement algorithm is in charge of giving a meaning to the terms,
types and proof terms directly written by the user or generated by using
tactics, decision procedures or general automation. The terms are written in an
"external syntax" meant to be user friendly that allows omission of
information, untyped binders and a certain liberal use of user defined
sub-typing. The refiner modifies the terms to obtain related well typed terms
in the internal syntax understood by the kernel of the ITP. In particular, it
acts as a type inference algorithm when all the binders are untyped. The
proposed algorithm is bi-directional: given a term in external syntax and a
type expected for the term, it propagates as much typing information as
possible towards the leaves of the term. Traditional mono-directional
algorithms, instead, proceed in a bottom-up way by inferring the type of a
sub-term and comparing (unifying) it with the type expected by its context only
at the end. We propose some novel bi-directional rules for CIC that are
particularly effective. Among the benefits of bi-directionality we have better
error message reporting and better inference of dependent types. Moreover,
thanks to bi-directionality, the coercion system for sub-typing is more
effective and type inference generates simpler unification problems that are
more likely to be solved by the inherently incomplete higher order unification
algorithms implemented. Finally we introduce in the external syntax the notion
of vector of placeholders that enables to omit at once an arbitrary number of
arguments. Vectors of placeholders allow a trivial implementation of implicit
arguments and greatly simplify the implementation of primitive and simple
tactics
Proof Outlines as Proof Certificates: A System Description
We apply the foundational proof certificate (FPC) framework to the problem of
designing high-level outlines of proofs. The FPC framework provides a means to
formally define and check a wide range of proof evidence. A focused proof
system is central to this framework and such a proof system provides an
interesting approach to proof reconstruction during the process of proof
checking (relying on an underlying logic programming implementation). Here, we
illustrate how the FPC framework can be used to design proof outlines and then
to exploit proof checkers as a means for expanding outlines into fully detailed
proofs. In order to validate this approach to proof outlines, we have built the
ACheck system that allows us to take a sequence of theorems and apply the proof
outline "do the obvious induction and close the proof using previously proved
lemmas".Comment: In Proceedings WoF'15, arXiv:1511.0252
The Problem of Analogical Inference in Inductive Logic
We consider one problem that was largely left open by Rudolf Carnap in his
work on inductive logic, the problem of analogical inference. After discussing
some previous attempts to solve this problem, we propose a new solution that is
based on the ideas of Bruno de Finetti on probabilistic symmetries. We explain
how our new inductive logic can be developed within the Carnapian paradigm of
inductive logic-deriving an inductive rule from a set of simple postulates
about the observational process-and discuss some of its properties.Comment: In Proceedings TARK 2015, arXiv:1606.0729
- …