6,016 research outputs found
Learning to Rank based on Analogical Reasoning
Object ranking or "learning to rank" is an important problem in the realm of
preference learning. On the basis of training data in the form of a set of
rankings of objects represented as feature vectors, the goal is to learn a
ranking function that predicts a linear order of any new set of objects. In
this paper, we propose a new approach to object ranking based on principles of
analogical reasoning. More specifically, our inference pattern is formalized in
terms of so-called analogical proportions and can be summarized as follows:
Given objects , if object is known to be preferred to , and
relates to as relates to , then is (supposedly) preferred to
. Our method applies this pattern as a main building block and combines it
with ideas and techniques from instance-based learning and rank aggregation.
Based on first experimental results for data sets from various domains (sports,
education, tourism, etc.), we conclude that our approach is highly competitive.
It appears to be specifically interesting in situations in which the objects
are coming from different subdomains, and which hence require a kind of
knowledge transfer.Comment: Thirty-Second AAAI Conference on Artificial Intelligence (AAAI-18), 8
page
Logic-Based Analogical Reasoning and Learning
Analogy-making is at the core of human intelligence and creativity with
applications to such diverse tasks as commonsense reasoning, learning, language
acquisition, and story telling. This paper contributes to the foundations of
artificial general intelligence by developing an abstract algebraic framework
for logic-based analogical reasoning and learning in the setting of logic
programming. The main idea is to define analogy in terms of modularity and to
derive abstract forms of concrete programs from a `known' source domain which
can then be instantiated in an `unknown' target domain to obtain analogous
programs. To this end, we introduce algebraic operations for syntactic program
composition and concatenation and illustrate, by giving numerous examples, that
programs have nice decompositions. Moreover, we show how composition gives rise
to a qualitative notion of syntactic program similarity. We then argue that
reasoning and learning by analogy is the task of solving analogical proportions
between logic programs. Interestingly, our work suggests a close relationship
between modularity, generalization, and analogy which we believe should be
explored further in the future. In a broader sense, this paper is a first step
towards an algebraic and mainly syntactic theory of logic-based analogical
reasoning and learning in knowledge representation and reasoning systems, with
potential applications to fundamental AI-problems like commonsense reasoning
and computational learning and creativity
From Analogical Proportion to Logical Proportions
International audienceGiven a 4-tuple of Boolean variables (a, b, c, d), logical proportions are modeled by a pair of equivalences relating similarity indicators ( aâ§b and aÂŻâ§bÂŻ), or dissimilarity indicators ( aâ§bÂŻ and aÂŻâ§b) pertaining to the pair (a, b), to the ones associated with the pair (c, d). There are 120 semantically distinct logical proportions. One of them models the analogical proportion which corresponds to a statement of the form âa is to b as c is to dâ. The paper inventories the whole set of logical proportions by dividing it into five subfamilies according to what they express, and then identifies the proportions that satisfy noticeable properties such as full identity (the pair of equivalences defining the proportion hold as true for the 4-tuple (a, a, a, a)), symmetry (if the proportion holds for (a, b, c, d), it also holds for (c, d, a, b)), or code independency (if the proportion holds for (a, b, c, d), it also holds for their negations (aÂŻ,bÂŻ,cÂŻ,dÂŻ)). It appears that only four proportions (including analogical proportion) are homogeneous in the sense that they use only one type of indicator (either similarity or dissimilarity) in their definition. Due to their specific patterns, they have a particular cognitive appeal, and as such are studied in greater details. Finally, the paper provides a discussion of the other existing works on analogical proportions
Ranking relations using analogies in biological and information networks
Analogical reasoning depends fundamentally on the ability to learn and
generalize about relations between objects. We develop an approach to
relational learning which, given a set of pairs of objects
,
measures how well other pairs A:B fit in with the set . Our work
addresses the following question: is the relation between objects A and B
analogous to those relations found in ? Such questions are
particularly relevant in information retrieval, where an investigator might
want to search for analogous pairs of objects that match the query set of
interest. There are many ways in which objects can be related, making the task
of measuring analogies very challenging. Our approach combines a similarity
measure on function spaces with Bayesian analysis to produce a ranking. It
requires data containing features of the objects of interest and a link matrix
specifying which relationships exist; no further attributes of such
relationships are necessary. We illustrate the potential of our method on text
analysis and information networks. An application on discovering functional
interactions between pairs of proteins is discussed in detail, where we show
that our approach can work in practice even if a small set of protein pairs is
provided.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS321 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Picking the one that does not fit - A matter of logical proportions
National audienceQuiz or tests about reasoning capabilities often pertain to the perception of similarity and dissimilarity between situations. Thus, one may be asked to complete a series of entities , , by an appropriate , or to pick the one that does not fit in a list. It has been shown that the first problem can receive a solution by solving analogical proportion equations between the representations of the entities in a logical setting, where we assume that should be such that is to as is to . In this paper, we focus on the second problem, and we show that it can be properly handled by means of heterogeneous proportions that are the logical dual of the homogeneous proportions involved in the modeling of analogical proportions and related proportions. Thus, the formal setting of logical proportions, to which homogeneous and heterogeneous proportions belong, provides an appropriate framework for handling the two problems in a coherent way. As it already exists for homogeneous proportions, a particular multiple-valued logic extension of heterogeneous proportions is discussed (indeed being an intruder in a group may be a matter of degree)
Bilingual analogical proportions via hedges
Analogical proportions are expressions of the form `` is to what
is to '' at the core of analogical reasoning which itself is at the core of
human and artificial intelligence. The author has recently introduced {\em from
first principles} an abstract algebro-logical framework of analogical
proportions within the general setting of universal algebra and first-order
logic. In that framework, the source and target algebras have the {\em same}
underlying language. The purpose of this paper is to generalize his unilingual
framework to a bilingual one where the underlying languages may differ. This is
achieved by using hedges in justifications of proportions. The outcome is a
major generalization vastly extending the applicability of the underlying
framework. In a broader sense, this paper is a further step towards a
mathematical theory of analogical reasoning
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