Premissary relevance

Premissary relevance is a property of arguments understood as speech act complexes. It is explicable in terms of the idea of a premise's lending support to a conclusion. Premissary relevance is a function of premises belonging to a set which authoritatively warrants an inference to a conclusion. An authoritative inference warrant will have associated with it a conditional proposition which is true— that is to say, which can be justified. The study of the Aristotelian doctrine of topoi or argument schemes may contribute to the task of identifying authoritative warrants.     

Generalizations of the partial,part and bipartial canonical correlation analysis

Theg ₁- andg ₂-bipartial canonical correlation analyses are developed as generalizations of the partial, part, and bipartial canonical correlation analysis. Illustrative examples are provided.     

Systematizing Toulmin’s Warrants: An Epistemic Approach

Relevance of premises to conclusion can be explicated through Toulmin’s notion of warrant, understood as an inference rule, albeit not necessarily formal. A normative notion of relevance requires the warrant to be reliable. To determine reliability, we propose a fourfold classification of warrants into a priori, empirical, institutional, and evaluative, with further subdivisions possible. This classification has its ancestry in classical rhetoric and recent epistemology. Distinctive to each type of warrant is the mode by which such connections are intuitively discovered and the grounds on which we ultimately justify them. The classification of warrants is thus epistemic. We illustrate the difference by contrasting empirical physical with institutional intuition, and argue for the advantages of this approach over Toulmin’s conception of field dependence.     

Induction,focused sampling and the law of small numbers

Hilary Kornblith (1993) has recently offered a reliabilist defense of the use of the Law of Small Numbers in inductive inference. In this paper I argue that Kornblith's defense of this inferential rule fails for a number of reasons. First, I argue that the sort of inferences that Kornblith seeks to justify are not really inductive inferences based on small samples. Instead, they are knowledge-based deductive inferences. Second, I address Kornblith's attempt to find support in the work of Dorrit Billman and I try to show that close attention to the workings of her computational model reveals that it does not support Kornblith's argument. While the knowledge required to ground the inferences in question is perhaps inductively derived, Billman's work does not support the notion that small samples provide a reliable basis for our generalizing inferences.     

Word, thought, and deed: the role of object categories in children's inductive inferences and exploratory play

Previous research (e.g., S. A. Gelman & E. M. Markman, 1986; A. Gopnik & D. M. Sobel, 2000) suggests that children can use category labels to make inductive inferences about nonobvious causal properties of objects. However, such inductive generalizations can fail to predict objects' causal properties when (a) the property being projected varies within the category, (b) the category is arbitrary (e.g., things smaller than a bread box), or (c) the property being projected is due to an exogenous intervention rather than intrinsic to the object kind. In 4 studies, the authors showed that preschoolers (M = 48 months; range = 42-57 months) were sensitive to these constraints on induction and selectively engaged in exploration when evidence about objects' causal properties conflicted with inductive generalizations from the objects' kind to their causal powers. This suggests that the exploratory actions children generate in free play could support causal learning.     

Tension-compression-tension tertiary twins in coarse-grained polycrystalline pure magnesium at room temperature

Using electron backscatter diffraction, the microstructural features of tension–compression–tension (T–C–T) tertiary twins are studied in coarse-grained pure polycrystalline magnesium subjected to monotonic compression along the extrusion direction in ambient air. T–C–T tertiary twins are developed due to the formation of a compression–tension double twin inside a primary tension twin. All the observed T–C–T twin variants are of T_iC_jT_j type. T_iC_i+1T_i+1 (or T_iC_i?1T_i?1) variants are observed more frequently than T_iC_i+2T_i+2 (or T_iC_i?2T_i?2) variants. The number of tertiary twin lamellae increases with the applied compressive strain.     

A note concerning the creager—Valentine paper

TheU _i statistic, discussed by Creager and Valentine in a recent paper, is defined as a standard error of estimate for the regression of a composite, consisting ofn components, on then–1 components, exclusive of thejth component. It is shown that this standard error equals the standard error of estimate for the prediction of thejth component from the othern–1 components. This equality is used to suggest an efficient procedure to compute all primary uniquenessesU _i .     

The number of paths and cycles in a digraph

An algorithm is presented for constructing from the adjacency matrix of a digraph the matrix of its simplen-sequences. In this matrix, thei, j entry,i j, gives the number of paths of lengthn from a pointv _i to a pointv _j ; the diagonal entryi, i gives the number of cycles of lengthn containingv _i . The method is then generalized to networks—that is, digraphs in which some value is assigned to each line. With this generalized algorithm it is possible, for a variety of value systems, to calculate the values of the paths and cycles of lengthn in a network and to construct its value matrix of simplen-sequences. The procedures for obtaining the two algorithms make use of properties of a line digraph—that is, a derived digraph whose points and lines represent the lines and adjacency of lines of the given digraph.The research reported here was supported by Grant NSF-G-17771 from the National Science Foundation. We wish to thank Professor Frank Harary for suggesting certain ways of improving an earlier draft of this paper.     

A Logic For Inductive Probabilistic Reasoning

Inductive probabilistic reasoning is understood as the application of inference patterns that use statistical background information to assign (subjective) probabilities to single events. The simplest such inference pattern is direct inference: from “70% of As are Bs” and “a is an A” infer that a is a B with probability 0.7. Direct inference is generalized by Jeffrey’s rule and the principle of cross-entropy minimization. To adequately formalize inductive probabilistic reasoning is an interesting topic for artificial intelligence, as an autonomous system acting in a complex environment may have to base its actions on a probabilistic model of its environment, and the probabilities needed to form this model can often be obtained by combining statistical background information with particular observations made, i.e., by inductive probabilistic reasoning. In this paper a formal framework for inductive probabilistic reasoning is developed: syntactically it consists of an extension of the language of first-order predicate logic that allows to express statements about both statistical and subjective probabilities. Semantics for this representation language are developed that give rise to two distinct entailment relations: a relation ⊨ that models strict, probabilistically valid, inferences, and a relation that models inductive probabilistic inferences. The inductive entailment relation is obtained by implementing cross-entropy minimization in a preferred model semantics. A main objective of our approach is to ensure that for both entailment relations complete proof systems exist. This is achieved by allowing probability distributions in our semantic models that use non-standard probability values. A number of results are presented that show that in several important aspects the resulting logic behaves just like a logic based on real-valued probabilities alone.     

The logic of ability,freedom and responsibility

The aim of this paper is to offer a rigorous explication of statements ascribing ability to agents and to develop the logic of such statements. A world is said to be feasible iff it is compatible with the actual past-and-present. W is a P-world iff W is feasible and P is true in W (where P is a proposition). P is a sufficient condition for Q iff every P world is a Q world. P is a necessary condition for Q iff Q is a sufficient condition forP. Each individual property S is shown to generate a rule for an agent X. X heeds S iff X makes all his future choices in accordance with S. (Note that X may heed S and yet fail to have it). S is a P-strategy for X iff X's heeding S together with P is a necessary and sufficient condition for X to have S. (P-strategies are thus rules which X is able to implement on the proviso P).Provisional opportunity: X has the opportunity to A provided P iff there is an S such that S is a P-strategy for X and X's implementing S is a sufficient condition for X's doing A. P is etiologically complete iff for every event E which P reports P also reports an etiological ancestry of E, and P is true. Categorical opportunity: X has the opportunity to A iff there is a P such that P is etiologically complete and X has the opportunity to A provided P. For X to have the ability to A there must not only be an appropriate strategy, but X must have a command of that strategy. X steadfastly intends A iff X intends A at every future moment at which his doing A is not yet inevitable. X has a command of S w.r.t. A and P iff X's steadfastly intending A together with P is a sufficient condition for X to implement S. Provisional ability: X can A provided P iff there is an S such that S is a P-strategy for X, X's implementing S is a sufficient condition for X's doing A, and X has a command of S w.r.t. A and P. Categorical ability: X can A iff there is a P such that P is etiologically complete and X can A provided P. X is free w.r.t. to A iff X can A and X can non- A. X is free iff there is an A such that X is free w.r.t. A.     

The Poznań school methodology of idealization and concretization from the point of view of a revised structuralist theory conception

My thesis is that some methodological ideas of the Pozna school, i.e., the principles of idealization and concretization (factualization), and the correspondence principle can be represented rather successfully using the relations of theoretization and specialization of revised structuralism.Let <n(i), t(j)> (i=1,...m, j=1,...k) denote the conceptual apparatus of a theory T, and a class M={} (i=1,...m, j=1,...k) the models of T. The n-components refer to the values of dependent variables and t-components to the values of independent variables of the theory. The n- and t-components in turn represent appropriate concepts. Consider T ^* as a conceptual enrichment of T with concepts <n(i ^*), t(j ^*)> (i<i ^* or j<j ^*) and models M ^*={<D ^*, n(i ^*), t(j ^*)>}. If the classes M and M ^* are suitably related, then the situation illustrates both the case of the theoretization-relation of (revised) structuralism and of the factualization-principle of the Pozna school.Assume now that the concepts n(i), t(j) of T for some i, j are operationalized using some special assumptions generating appropriate empirical values n and t for these concepts. Let M denote the class {<D,...n,...t,...>} which is formed by substituting n and t for values of concepts n(i), t(j) in the elements of M. If the classes M and M are related in a suitable way then the situation is an example of both the specialization-relation of (revised) structuralism and the concretization-principle of the Pozna school. The correspondence principle in turn can be represented as a limiting case of the theoretization-relation of (revised) structuralism.Many thanks to my anonymous referees for critical and fruitful comments and special thanks to Dr. Carol Norris for correcting the language of this paper.     

Knowledge, expectations, and inductive reasoning within conceptual hierarchies

Previous research (e.g. Cognition 64 (1997) 73) suggests that the privileged level for inductive inference in a folk biological conceptual hierarchy does not correspond to the “basic” level (i.e. the level at which concepts are both informative and distinct). To further explore inductive inference within conceptual hierarchies, we examine relations between knowledge of concepts at different hierarchical levels, expectations about conceptual coherence, and inductive inference. In Experiments 1 and 2, 5- and 8-year-olds and adults listed features of living kind (Experiments 1 and 2) and artifact (Experiment 2) concepts at different hierarchical levels (e.g. plant, tree, oak, desert oak), and also rated the strength of generalizations to the same concepts. For living kinds, the level that showed a relative advantage on these two tasks differed; the greatest increase in features listed tended to occur at the life-form level (e.g. tree), whereas the greatest increase in inductive strength tended to occur at the folk-generic level (e.g. oak). Knowledge and induction also showed different developmental trajectories. For artifact concepts, the levels at which the greatest gains in knowledge and induction occurred were more varied, and corresponded more closely across tasks. In Experiment 3, adults reported beliefs about within-category similarity for concepts at different levels of animal, plant and artifact hierarchies, and rated inductive strength as before. For living kind concepts, expectations about category coherence predicted patterns of inductions; knowledge did not. For artifact concepts, both knowledge and expectations predicted patterns of induction. Results suggest that beliefs about conceptual coherence play an important role in guiding inductive inference, that this role may be largely independent of specific knowledge of concepts, and that such beliefs are especially important in reasoning about living kinds.     

A Statistical Hypothesis Testing Method for the Rank Ordering of the Priorities of the Alternatives in the Analytic Hierarchy Process

In analytic hierarchy process (AHP), a ratio scale (π₁, π₂, ⋯, π_t) for the priorities of the alternatives {T₁, T₂, ⋯, T_t} is used for a decision problem in which π_i/π_j is used to quantify the ratio of the priority of T_i to that of T_j. In a group decision‐making setup, the subjective estimates of π_i/π_j are obtained as entries of a pairwise comparison matrix for each member of the group. On the basis of these pairwise comparison matrices, one of the topics of interest in some situation is the total rank ordering of the priorities of the alternatives. In this article, a statistical method is proposed for testing a specific total rank ordering of the priorities of the alternatives. The method developed is then illustrated using numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Reversing the Counterfactual Analysis of Causation

The counterfactual analysis of causation has focused on one particular counterfactual conditional, taking as its starting‐point the suggestion that C causes E iff (～C □→ ～E). In this paper, some consequences are explored of reversing this counterfactual, and developing an account starting with the idea that C causes E iff (～E □→ ～C). This suggestion is discussed in relation to the problem of pre‐emption. It is found that the ‘reversed’ counterfactual analysis can handle even the most difficult cases of pre‐emption with only minimal complications. The paper closes with a discussion of the wider philosophical implications of developing a reversed counterfactual analysis, especially concerning the differentiation of causes from causal conditions, causation by absences, and the extent to which causes suffice for their effects.     

Instability, Modus ponens and uncertainty of deduction

Considering the instability of nonlinear dynamics, the deductive inference rule Modus ponens itself is not enough to guarantee the validity of reasoning sequences in the real physical world, and similar results cannot necessarily be obtained from similar causes. Some kind of stability hypothesis should be added in order to draw meaningful conclusions. Hence, the uncertainty of deductive inference appears to be like that of inductive inference, and the asymmetry between deduction and induction becomes unrecognizable such as to undermine the basis for the fundamental cleavage between analytic truth and synthetic truth, as W. V. O. Quine pointed out. Induction is not inferior to deduction from a pragmatic point of view.     

A quasi-nonmetric method for multidimensional scaling VIA an extended euclidean model

An Extended Two-Way Euclidean Multidimensional Scaling (MDS) model which assumes both common and specific dimensions is described and contrasted with the standard (Two-Way) MDS model. In this Extended Two-Way Euclidean model then stimuli (or other objects) are assumed to be characterized by coordinates onR common dimensions. In addition each stimulus is assumed to have a dimension (or dimensions) specific to it alone. The overall distance between objecti and objectj then is defined as the square root of the ordinary squared Euclidean distance plus terms denoting the specificity of each object. The specificity,s _j , can be thought of as the sum of squares of coordinates on those dimensions specific to objecti, all of which have nonzero coordinatesonly for objecti. (In practice, we may think of there being just one such specific dimension for each object, as this situation is mathematically indistinguishable from the case in which there are more than one.)We further assume that _ij =F(d _ij ) +e _ij where _ij is the proximity value (e.g., similarity or dissimilarity) of objectsi andj,d _ij is the extended Euclidean distance defined above, whilee _ij is an error term assumed i.i.d.N(0, ²).F is assumed either a linear function (in the metric case) or a monotone spline of specified form (in the quasi-nonmetric case). A numerical procedure alternating a modified Newton-Raphson algorithm with an algorithm for fitting an optimal monotone spline (or linear function) is used to secure maximum likelihood estimates of the paramstatistics) can be used to test hypotheses about the number of common dimensions, and/or the existence of specific (in addition toR common) dimensions.This approach is illustrated with applications to both artificial data and real data on judged similarity of nations.     

Predictive probability and analogy by similarity in inductive logic

The-continuum of inductive methods was derived from an assumption, called-condition, which says that the probability of finding an individual having propertyx _j depends only on the number of observed individuals having propertyx _j and on the total number of observed individuals. So, according to that assumption, all individuals with properties which are different fromx _j have equal weight with respect to that probability and, in particular, it does not matter whether any individual was observed having some propertysimilar tox _j (the most complete proof of this result is presented in Carnap, 1980).The problem thus remained open to find some general condition, weaker than the-condition, which would allow for thederivation of probability functions which might be sensitive to similarity. Carnap himself suggested a weakening of the-condition which might allow for similarity sensitive probability functions (Carnap, 1980, p. 45) but he did not find the family of probability functions derivable from that principle. The aim of this paper is to present the family of probability functions derivable from Carnap's suggestion and to show how it is derived.In Section 1 the general problem of analogy by similarity in inductive logic is presented, Section 2 outlines the notation and the conceptual background involved in the proof, Section 3 gives the proof, Section 4 discusses Carnap's principle and the result, Section 5 is a brief review of the solutions which have previously been proposed.     

Conceptual influences on induction: A case for a late onset

This research examines the mechanism of early induction, the development of induction, and the ways attentional and conceptual factors contribute to induction across development. Different theoretical views offer different answers to these questions. Six experiments with 4- and 5-year-olds, 7-year-olds and adults (N = 208) test these competing theories by teaching categories for which category membership and perceptual similarity are in conflict, and varying orthogonally conceptual and attentional factors that may potentially affect inductive inference. The results suggest that early induction is similarity-based; conceptual information plays a negligible role in early induction, but its role increases gradually, with the 7-year-olds being a transitional group. And finally, there is substantial contribution of attention to the development of induction: only adults, but not children, could perform category-based induction without attentional support. Therefore, category-based induction exhibits protracted development, with attentional factors contributing early in development and conceptual factors contributing later in development. These results are discussed in relation to existing theories of development of inductive inference and broader theoretical views on cognitive development.     

Sample selection and inductive generalization

In two experiments with adults (N=126), we examined the influence of sampling procedure on inductive generalization. In predicate sampling, participants learned the category identity of individuals known to possess some property. In subject sampling, individuals selected for category identity were discovered to possess a novel property. In both experiments, sampling procedure influenced induction. Predicate sampling resulted in very narrow generalization, whereas subject sampling yielded a fairly high and constant rate of projection. Differences in confidence of generalizations were also observed. Conditions in which evidence was described as randomly sampled from a collection of animals yielded a consistent decrease in projections as predicted by similarity-based models. The results are presented as support for an evidence-based view of induction.