Learning processes in matching and oddity: the oddity preference effect and sample reinforcement

Eight pigeons learned either matching (to sample) or oddity (from sample) with or without reward for sample responding. The training stimuli were coarse-white, fine-black, or smooth-mauve gravels in pots with buried grain as the reinforcer. Oddity without sample reward was learned most rapidly, followed by matching with sample reward, oddity with sample reward, and matching without sample reward. Transfer was related to acquisition rate: The oddity group without sample reward showed full (equal to baseline) color and texture transfer; the matching group with sample reward showed partial texture transfer; other groups showed no transfer. Sample reward was shown to determine rate of acquisition of matching and oddity and the oddity preference effect. The results are discussed in terms of item-specific associations operating early in learning prior to any relational learning between sample and comparison stimuli.     

Synonymy and Intra-Theoretical Pluralism

The starting point of this paper is a version of intra-theoretical (logical) pluralism that was recently proposed by Hjortland [2013]. In a first move, I use synonymy-relations to formulate an intuitively compelling objection against Hjortland's claim that, if one uses a single calculus to characterise the consequence relations of the paraconsistent logic LP and the paracomplete logic K3, one immediately obtains multiple consequence relations for a single language and hence a reply to the Quinean charge of meaning variance. In a second move, I explain how a natural generalisation of the notion of synonymy (adapted to the 3-sided sequent-calculus used by Hjortland) can be used to counter this objection, but I also show how the solution can be turned into an equally devastating ‘one logic after all’ type of objection. Finally, I propose the general diagnosis that these problems could only arise in the presence of conceptual distinctions that are too coarse to accommodate coherent pluralist theses. The latter leads to the general methodological recommendation that the conceptual resources used to think and talk about logic should be kept in line with the formal resources that are used to define and describe a logical theory.     

Logics of Synonymy

Journal of Philosophical Logic - We investigate synonymy in the strong sense of content identity (and not just meaning similarity). This notion is central in the philosophy of language and in...     

Synonymy and the epistemology of linguistics

In Word and Object, Quine argues from the observation that ‘there is no justification for collating linguistic meanings, unless in terms of men's dispositions to respond overtly to socially observable stimulations’ to the conclusion that ‘the enterprise of translation is found to be involved in a certain systematic indeterminacy’. In this paper, I propose to show (1) that Quine's thesis, when properly understood, reveals in the situation of translation no peculiar indeterminacy but merely the ordinary indeterminacy present in any case of empirical investigation; (2) that it is plausible that, because the subject of inquiry is language, we are in a better position with respect to such empirical indeterminacies than we are in other areas of investigation; (3) that, in any case, Quine's arguments are impotent, for they are either contradictory or incoherent; and (4) that Quine is led to his radical conclusions because he confuses a trivial and unexciting indeterminacy, which does obtain, with the striking indeterminacy for which he argues, which does not obtain.     

A Quinean Definition Of Synonymy

The main purpose of this paper is to propose and defend anew definition of synonymy. Roughly (and slightly misleadingly), theidea is that two expressions are synonymous iff intersubstitutions insentences preserve the degree of doxastic revisability. In Section 1 Iargue that Quine's attacks on analyticity leave room for such adefinition. The definition is presented in Section 2, and Section 3elaborates on the concept of revisability. The definition is defendedin Sections 4 and 5. It is, inter alia, shown that the definition hasdesired formal properties. In Sections 6 and 7 I briefly comment on,first, the relation of the definition to Quine's later ideas about (stimulus)synonymy, and, second, its relation to a general, interlinguistic, conceptof meaning.     

语境同义性逻辑(英文)

众所周知,基于可能世界语义的内涵逻辑由于对意义的刻画过于粗粝而导致了所谓的"超内涵问题"。为了解决超内涵问题,出现了各种超内涵逻辑,其中由Suszko提出的带等词的命题逻辑(SCI)是超内涵逻辑中最基本的一种。本文是对SCI的精炼,其动机是语境同义性论题(CST)。该论题认为,同义性标准具有语境依赖性。基于认知语境主义,我们给出了CST的一个论证。通过将SCI中的二元等词修改为一个三元结构,用来表示两个陈述相对某个语境表达同一命题,我们给出了CST的希尔伯特式公理系统。我们证明了该系统相对一个代数模型类是可靠的和完全的。该代数模型的论域由命题构成,同时附带一组命题上的全等关系,用以刻画相对于语境的命题同一性。我们运用该逻辑部分解决了分析悖论这一困扰逻辑学家多年的问题。与我们之前的基于相同动机的论文[17]相比,本文给出的形式语言更加丰富,从而能够表达不同语境之间以及不同语境的同义性之间的关系。     

Zipf's Law and Avoidance of Excessive Synonymy

Zipf's law states that if words of language are ranked in the order of decreasing frequency in texts, the frequency of a word is inversely proportional to its rank. It is very reliably observed in the data, but to date it escaped satisfactory theoretical explanation. This article suggests that Zipf's law may result from a hierarchical organization of word meanings over the semantic space, which in turn is generated by the evolution of word semantics dominated by expansion of meanings and competition of synonyms. A study of the frequency of partial synonyms in Russian provides experimental evidence for the hypothesis that word frequency is determined by semantics.     

Temporal sequence effects in auditory oddity discrimination

The oddity method was used in assessing pitch, loudness, simultaneous tone, successive tone, and speech sound discrimination in 35 normal children and 15 children with learning problems. With this method three auditory stimuli are presented, two of which are identical, and the S is required to indicate the temporal position of the odd stimulus. For both groups, discrimination was most accurate when the odd stimulus was in the third position. These results could be explained by assuming that the oddity response was based upon successive Same-Different judgments of the first and second stimuli and the second and third stimuli, since a correct response to third-position oddity would require only a Same judgment of the first and second stimuli. Other findings were not as easily explained by this simple model, and alternative hypotheses are discussed.     

Concurrent performances: rate and accuracy of free-operant oddity responding

In pigeon's oddity performances, maintained by variable-interval reinforcement of pecks on the odd key of three keys in a triangular array, accuracy and response rate varied inversely with the rate of variable-interval reinforcement scheduled concurrently for pecks on a fourth, spatially isolated key. But when variable-interval and extinction components alternated in a multiple schedule for pecks on the spatially isolated key, oddity accuracy was greater during variable-interval components than during extinction components. Oddity response rate was not affected systematically by the alternating components. Changeovers between the oddity keys and the spatially isolated key were frequent during variable-interval components; responding occurred almost exclusively on the oddity keys during extinction components. This difference in performance during the two components was eliminated by arranging stimulus-correlated variable-interval reinforcement in the multiple schedule on the spatially isolated key: a stimulus was presented in the variable-interval components only when reinforcement became available, thereby reducing responding on this key to near-zero levels in both components while maintaining the variable-interval reinforcement. The effect of the multiple-schedule components on oddity accuracy was not altered, however, and thus apparently depended directly on concurrent reinforcement and not on differential sequential properties of concurrent responding during the two components.     

The optimum decision rules for the oddity task

This paper presents the optimum decision rule for an m-interval oddity task in whichm-1 intervals contain the same signal and one is different or odd. The optimum decision rule depends on the degree of correlation among observations. The present approach unifies the different strategies that occur with “roved” or “fixed” experiments (Macmillan & Creelman, 1991, p. 147). It is shown that the commonly used decision rule for anm-interval oddity task corresponds to the special case of highly correlated observations. However, as is also true for thesame-different paradigm, there exists a different optimum decision rule when the observations are independent. The relation between the probability of a correct response andd’ is derived for the three-interval oddity task. Tables are presented of this relation for the three-, four-, and five-interval oddity task. Finally, an experimental method is proposed that allows one to determine the decision rule used by the observer in an oddity experiment.     

Analyticity Without Synonymy In Simple Comparative Logic

In this paper I provide some formal schemas for theanalysis of vague predicatesin terms of a set of semantic relations other thanclassical synonymy, includingweak synonymy (as between ``large' and ``huge'),antonymy (as between ``large'and ``small'), relativity (as between ``large'and ``large for a dog'), and a kind ofsupervenience (as between ``large' and ``wide'or ``long'). All of these relationsare representable in the simple comparativelogic CL, in accordance with the basicformula: the more something is F, the more(or less) it is G. I use Carnapianmeaning postulates to define these relationsas constraints on interpretations of theformal language of CL.     

Comparison of two oddity tasks with pigeons

Two oddity tasks were compared: one in which the odd stimulus could appear on any of the three stimulus positions (true oddity); the other in which the odd stimulus could only appear on the left or right but not the center (oddity-from-sample). A stimulus-configuration theory predicts faster oddity-from-sample learning, whereas a theory, based on shifts in observing over trials, predicts faster learning of true oddity. Pigeons learned the oddity-from-sample task faster, thus supporting configuration theory. Performance on the oddity-from-sample task but not the true oddity task was facilitated by increasing the number of responses required to terminate a trial. When the oddity-from-sample pigeons were shifted to the true oddity task, no evidence of positive transfer was found, suggesting that a configuration theory alone is insufficient to explain differences in acquisition. Only when a correction procedure was introduced did the true oddity pigeons perform above 50%.     

Synonymy in sentential languages: a pragmatic view

In this note two notions of meaning are considered and accordingly two versions of synonymy are defined, weaker and stronger ones. A new semantic device is introduced: a matrix is said to be pragmatic iff its algebra is in fact an algebra of meanings in the stronger sense. The new semantics is proved to be universal enough (Theorem 1), and it turns out to be in some sense a generalization of Wójcicki's referential semantics (Theorem 3).     

Effects of fixed-ratio sample and choice response requirements upon oddity matching

Three pigeons were trained on oddity matching in which either 1, 4, 8, 16, or 32 sample-key observing responses were required to turn off the sample stimuli and turn on the comparison stimuli. Oddity accuracy increased when the observing-response requirement was raised and decreased when the requirement was lowered. Next, while the observing requirement was maintained at one response, the number of responses required to the comparison stimuli was either 1, 4, 8, 16, or 32. Under these conditions, choice was defined as the comparison that first accumulated the required number of responses. In general, increasing the comparison-response requirement decreased accuracy and lowering the comparison requirement increased accuracy. The fixed-ratio observing requirements appeared to facilitate control by stimuli serving an instructional function.     

Use of number by crows: investigation by matching and oddity learning

Hooded crows were trained in two-alternative simultaneous matching and oddity tasks with stimulus sets of three different categories: color (black and white), shape (Arabic Numerals 1 and 2, which were used as visual shapes only), and number of elements (arrays of one and two items). These three sets were used for training successively and repeatedly; the stimulus set was changed to the next one after the criterion (80% correct or better over 30 consecutive trials) was reached with the previous one. Training was continued until the criterion could be reached within the first 30 to 50 trials for each of the three training sets. During partial transfer tests, familiar stimuli (numerals and arrays in the range from 1 to 2) were paired with novel ones (numerals and arrays in the range from 3 to 4). At the final stage of testing only novel stimuli were presented (numerals and arrays in the range from 5 to 8). Four of 6 birds were able to transfer in these tests, and their performance was significantly above chance. Moreover, performance of the birds on the array stimuli did not differ from their performance on the color or shape stimuli. They were capable of recognizing the number of elements in arrays and comparing the stimuli by this attribute. It was concluded that crows were able to apply the matching (or oddity) concept to stimuli of numerical category.