4,661 research outputs found
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
Hints towards the Emergent Nature of Gravity
A possible way out of the conundrum of quantum gravity is the proposal that
general relativity (GR) is not a fundamental theory but emerges from an
underlying microscopic description. Despite recent interest in the emergent
gravity program within the physics as well as the philosophy community, an
assessment of the theoretical evidence for this idea is lacking at the moment.
We intend to fill this gap in the literature by discussing the main arguments
in favour of the hypothesis that the metric field and its dynamics are
emergent. First, we distinguish between microstructure inspired from GR, such
as through quantization or discretization, and microstructure that is not
directly motivated from GR, such as strings, quantum bits or condensed matter
fields. The emergent gravity approach can then be defined as the view that the
metric field and its dynamics are derivable from the latter type of
microstructure. Subsequently, we assess in how far the following properties of
(semi-classical) GR are suggestive of underlying microstructure: (1) the
metric's universal coupling to matter fields, (2) perturbative
non-renormalizability, (3) black hole thermodynamics, and (4) the holographic
principle. In the conclusion we formalize the general structure of the
plausibility arguments put forward.Comment: 36 pages, v2: minor additions, references added. Journal version in
Studies in History and Philosophy of Modern Physic
A new 3D-beam finite element including non-uniform torsion with the secondary torsion moment deformation effect
In this paper, a new 3D Timoshenko linear-elastic beam finite element including warping torsion will be presented which is suitable for analysis of spatial structures consisting of constant open and hollow structural section (HSS) beams. The analogy between the 2ndorder beam theory (with axial tension) and torsion (including warping) was used for the formulation of the equations for non-uniform torsion. The secondary torsional moment deformation effect and the shear force effect are included into the local beam finite element stiffness matrix. The warping part of the first derivative of the twist angle was considered as an additional degree of freedom at the finite element nodes. This degree of freedom represents a part of the twist angle curvature caused by the bimoment. Results of the numerical experiments are discussed, compared and evaluated. The importance of the inclusion of warping in stress-deformation analyses of closed-section beams is demostrated
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Reasoning under uncertainty: the role of two informal fallacies in an emerging scientific inquiry
It is now commonplace in fallacy inquiry for many of the traditional informal fallacies to be viewed as reasonable or non-fallacious modes of argument. Central to this evaluative shift has been the attempt to examine traditional fallacies within their wider contexts of use. However, this pragmatic turn in fallacy evaluation is still in its infancy. The true potential of a contextual approach in the evaluation of the fallacies is yet to be explored. I examine how, in the context of scientific inquiry, certain traditional fallacies function by conferring epistemic gains upon inquiry. Specifically, I argue that these fallacies facilitate the progression of inquiry, particularly in the initial stages of inquiry when the epistemic context is one of uncertainty. The conception of these fallacies that emerges is that of heuristics of reasoning in contexts of epistemic uncertainty
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The effect of multiple knowledge sources on learning and teaching
Current paradigms for machine-based learning and teaching tend to perform their task in isolation from a rich context of existing knowledge. In contrast, the research project presented here takes the view that bringing multiple sources of knowledge to bear is of central importance to learning in complex domains. As a consequence teaching must both take advantage of and beware of interactions between new and existing knowledge. The central process which connects learning to its context is reasoning by analogy, a primary concern of this research. In teaching, the connection is provided by the explicit use of a learning model to reason about the choice of teaching actions. In this learning paradigm, new concepts are incrementally refined and integrated into a body of expertise, rather than being evaluated against a static notion of correctness. The domain chosen for this experimentation is that of learning to solve "algebra story problems." A model of acquiring problem solving skills in this domain is described, including: representational structures for background knowledge, a problem solving architecture, learning mechanisms, and the role of analogies in applying existing problem solving abilities to novel problems. Examples of learning are given for representative instances of algebra story problems. After relating our views to the psychological literature, we outline the design of a teaching system. Finally, we insist on the interdependence of learning and teaching and on the synergistic effects of conducting both research efforts in parallel
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Machine learning : techniques and foundations
The field of machine learning studies computational methods for acquiring new knowledge, new skills, and new ways to organize existing knowledge. In this paper we present some of the basic techniques and principles that underlie AI research on learning, including methods for learning from examples, learning in problem solving, learning by analogy, grammar acquisition, and machine discovery. In each case, we illustrate the techniques with paradigmatic examples
The development of renormalization group methods for particle physics: Formal analogies between classical statistical mechanics and quantum field theory
Analogies between classical statistical mechanics (CSM) and quantum field theory (QFT) played a pivotal role in the development of renormalization group (RG) methods for application in the two theories. This paper focuses on the analogies that informed the application of RG methods in QFT by Kenneth Wilson and collaborators in the early 1970's (Wilson and Kogut 1974). The central task that is accomplished is the identification and analysis of the analogical mappings employed. The conclusion is that the analogies in this case study are formal analogies, and not physical analogies. That is, the analogical mappings relate elements of the models that play formally analogous roles and that have substantially different physical interpretations. Unlike other cases of the use of analogies in physics, the analogical mappings do not preserve causal structure. The conclusion that the analogies in this case are purely formal carries important implications for the interpretation of QFT, and poses challenges for philosophical accounts of analogical reasoning and arguments in defence of scientific realism. Analysis of the interpretation of the cutoffs is presented as an illustrative example of how physical disanalogies block the exportation of physical interpretations from from statistical mechanics to QFT. A final implication is that the application of RG methods in QFT supports non-causal explanations, but in a different manner than in statistical mechanics
The development of renormalization group methods for particle physics: Formal analogies between classical statistical mechanics and quantum field theory
Analogies between classical statistical mechanics (CSM) and quantum field theory (QFT) played a pivotal role in the development of renormalization group (RG) methods for application in the two theories. This paper focuses on the analogies that informed the application of RG methods in QFT by Kenneth Wilson and collaborators in the early 1970's (Wilson and Kogut 1974). The central task that is accomplished is the identification and analysis of the analogical mappings employed. The conclusion is that the analogies in this case study are formal analogies, and not physical analogies. That is, the analogical mappings relate elements of the models that play formally analogous roles and that have substantially different physical interpretations. Unlike other cases of the use of analogies in physics, the analogical mappings do not preserve causal structure. The conclusion that the analogies in this case are purely formal carries important implications for the interpretation of QFT, and poses challenges for philosophical accounts of analogical reasoning and arguments in defence of scientific realism. Analysis of the interpretation of the cutoffs is presented as an illustrative example of how physical disanalogies block the exportation of physical interpretations from from statistical mechanics to QFT. A final implication is that the application of RG methods in QFT supports non-causal explanations, but in a different manner than in statistical mechanics
Influencia del nivel educativo de los progenitores y la edad en la derivación de equivalencia-equivalencia
Antecedentes: el objetivo de este trabajo fue el estudio del razonamiento analógico desde el fenómeno de equivalencia-equivalencia. Método: las variables estudiadas fueron la edad de los participantes y el nivel educativo de los padres, en relación a la ejecución de la tarea de razonamiento. Para ello se utilizó una muestra de 64 participantes. Se diseñó un instrumento basado en discriminaciones condicionales utilizando el procedimiento de igualación simbólica a la muestra. Resultados: los resultados mostraron una diferencia significativa en la ejecución de la tarea entre los niños con padres universitarios y los niños con padres no universitarios. Sin embargo, en relación a la edad no se obtuvieron resultados concluyentes. Conclusiones: se analizan estos resultados desde la perspectiva de la derivación de la relación de equivalencia-equivalencia a través de entrenamiento en múltiples ejemplares como origen de la derivación del fenómeno.Background: The objective of this work was the study of analogical reasoning from the perspective of the equivalence-equivalence phenomenon. Method: The variables studied consisted of the age of the participants and the educational level of the parents, in relation to performance on a reasoning task. The task utilized a sample size of 64 participants and an instrument based on conditional discriminations using the matching-to-sample procedure. Results: The results showed a significant difference in the performance on the task between the children of parents with college degrees, and those of parents without college degrees. However, there were no conclusive results as to age. Conclusions: The results are analyzed from the perspective of the derivation of the relationship of equivalence-equivalence via multiple exemplar training
Building and Refining Abstract Planning Cases by Change of Representation Language
ion is one of the most promising approaches to improve the performance of
problem solvers. In several domains abstraction by dropping sentences of a
domain description -- as used in most hierarchical planners -- has proven
useful. In this paper we present examples which illustrate significant
drawbacks of abstraction by dropping sentences. To overcome these drawbacks, we
propose a more general view of abstraction involving the change of
representation language. We have developed a new abstraction methodology and a
related sound and complete learning algorithm that allows the complete change
of representation language of planning cases from concrete to abstract.
However, to achieve a powerful change of the representation language, the
abstract language itself as well as rules which describe admissible ways of
abstracting states must be provided in the domain model. This new abstraction
approach is the core of Paris (Plan Abstraction and Refinement in an Integrated
System), a system in which abstract planning cases are automatically learned
from given concrete cases. An empirical study in the domain of process planning
in mechanical engineering shows significant advantages of the proposed
reasoning from abstract cases over classical hierarchical planning.Comment: See http://www.jair.org/ for an online appendix and other files
accompanying this articl
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