Arithmetic based on the Church numerals in illative combinatory logic

In the early thirties, Church developed predicate calculus within a system based on lambda calculus. Rosser and Kleene developed Arithmetic within this system, but using a Godelization technique showed the system to be inconsistent.Alternative systems to that of Church have been developed, but so far more complex definitions of the natural numbers have had to be used. The present paper based on a system of illative combinatory logic developed previously by the author, does allow the use of the Church numerals. Given a new definition of equality all the Peano-type axioms of Mendelson except one can be derived. A rather weak extra axiom allows the proof of the remaining Peano axiom. Note. The illative combinatory logic used in this paper is similar to the logic employed in computer languages such as ML.The author wishes to thank Dr. Roger Hindley for proofreading this paper and for making some useful suggestions. This paper was presented at the 1986 Annual Conference of the Australasian Association of Logic in Auckland, 9–12 July, 1986.     

A representation theorem for languages with generalized quantifiers through back-and-forth methods

We obtain in this paper a representation of the formulae of extensions ofL by generalized quantifiers through functors between categories of first-order structures and partial isomorphisms. The main tool in the proofs is the back-and-forth technique. As a corollary we obtain the Caicedo's version of Fraïssés theorem characterizing elementary equivalence for such languages. We also discuss informally some geometrical interpretations of our results.     

Fuzziness of concepts and concepts of fuzziness

It has been a vexing question in recent years whether concepts are fuzzy. In this paper several views on the fuzziness of concepts are pointed out to have stemmed from dubious concepts of fuzziness. The underlying notions of the roles feasibly played byprototype, set, andprobability in modeling concepts strongly suggest that the controversy originates from a vague relation between intuitive and mathematical ideas in the cognitive sciences. It is argued that the application of fuzzy sets cannot resolve this vagueness since they are one sided,viz., defined on sets. An alternative definition based on classes (in the sense of axiomatic set theory) is proposed.     

Closed-class words as first syllables do interfere with lexical decisions for nonwords: implications for theories of agrammatism

It has been proposed that a principal cause of the agrammatism of some Broca's aphasics is that such patients, unlike normal subjects, are unable to make use of a special retrieval mechanism for closed-class ("function") words (D. C. Bradley, 1978, Computational distinctions of vocabulary type, Unpublished Ph.D. thesis; D. C. Bradley, M. F. Garrett, & E. B. Zurif, 1980. In D. Caplan (Ed.), Biological studies of mental processes). The main evidence for the existence of such a mechanism consisted of two observations: (1) the recognition of open-class words was observed to be frequency-sensitive, but that of closed-class words was not; and (2) lexical decisions for nonwords which began with open-class words were delayed, whereas there was no such interference for nonwords which began with closed-class words. However, the first of these observations has proved nonreplicable (e.g., B. Gordon & A. Caramazza, 1982, Brain and Language, 15, 143-160, 1983, Brain and Language, 19, 335-345; J. Segui, J. Mehler, W. Frauenfelder, & J. Morton, 1982, Neuropsychologia, 20, 615-627), and in the present paper, three lexical decision experiments are reported in which it is found that, when certain confounding variables are controlled, nonwords which begin with closed-class words are subject to interference. Moreover, contrary to a suggestion of Kolk and Blomert (1985, Brain and Language, 26, 94-105) the interference is independent of the presence of closed-class items in the lexical decision word list. It seems, then, that closed-class words are not qualitatively different from open-class words with respect either to frequency sensitivity or to nonword interference, and in consequence, the above proposed explanation of agrammatism is left without major empirical support.     

Perceptions of speakers with minimal eye contact: Implications for stutterers

One hundred and thirty-three college students responded to percentage definitions of “good,” “minimal,” and “no” eye contact. They also judged their perceptions of a speaker with “little or no eye contact” on a semantic differential scale containing 60 polarized adjective pairs regarding personality traits. The majority of the student respondents defined an individual with “good” eye contact as looking at his/her audience/listener 90–100% of the time. This is a more stringent definition than other literature has indicated. Furthermore, speakers with little or no eye contact were judged less favorably on 70% of the items, which indicates that low eye contact adversely affects perceptions of a speaker's personality. Therefore, stutterers need to be made aware of the importance of and determinants of effective eye contact in communication. Also, the development of effective eye contact needs to be incorporated as a major goal in stuttering therapy.     

Selective attention: effects of cuing on the processing of different types of compound stimuli

Pigeons in a matching-to-sample experiment received (a) element samples (one of two colors or vertical or horizontal white lines), (b) separated compound samples (a color and a line element presented together), and (c) unified compound samples (vertical or horizontal colored lines). In Phase I, test stimuli were the two elements from one dimension; the dimension tested varied randomly when the sample was a compound. Element samples were matched better than unified samples, which were matched better than separated samples. In Phase II, two samples preceded the tests. On EC trials, the first sample (S1) was an element, and the second sample (S2) was a compound; on CE trials this order was reversed. One element of the compound sample was always the one appearing as the element sample on that trial (e.g., S1 = red, S2 = red-vertical). This element also served as the correct test alternative (e.g., test = red+ vs. green) except on probe trials when the correct test was the other element appearing in the compound (e.g., test = vertical+ vs. horizontal). Accuracy varied as a function of sample sequence when the compound was separated (EC greater than CE on nonprobe trials and CE greater than EC on prove trials). This pattern was not observed when the compound was unified. The data suggest that the element in EC trials served as a cue that increased processing of the cued dimension and decreased processing of the noncued dimension of separated compounds. However, both dimensions of unified compounds seem to have been processed regardless of cuing.(ABSTRACT TRUNCATED AT 250 WORDS)     

Cerebral hemispheric mechanisms in the retrieval of ambiguous word meanings

Targets related to ambiguous primes were projected to the left and right visual fields in a lexical priming experiment with stimulus onset asynchronies (SOA) of 35 and 750 msec. Right visual field results were similar to our earlier results with central projection (G. B. Simpson & C. Burgess, 1985, Journal of Experimental Psychology: Human Perception and Performance, 11, 28-39). Facilitation was found for the more frequent meaning at both SOAs and a decrease in facilitation for the less frequent meaning at the longer SOA. In contrast, left visual field results indicated a decay of facilitation for the more frequent meaning at the longer SOA, while activation for the subordinate meaning increased. Results suggest that, while automatic processing occurs in both hemispheres, only the left hemisphere engages in controlled processing of ambiguous word meanings. In addition, the present results support the idea that the right hemisphere has a special role in ambiguity resolution and that the right hemisphere lexicon possesses a richer endowment than earlier thought.     

Role of the area postrema in three putative measures of motion sickness in the rat

After thermal cauterization of the area postrema in rats the absence of conditioned taste aversion to sucrose paired with lithium chloride (0.15 M, 3.3 ml/kg) was used as a pharmacologic/behavioral index of area postrema damage. In a subsequent experiment the effects of area postrema lesions on three measures proposed as species-relevant measures of motion sickness were studied, using off-vertical rotation at 150 degrees/s for either 30 or 90 min. Lesions of area postrema did not alter postrotational suppression of drinking or amount of defecation during motion. The initial acquisition of conditioned taste aversion to a novel cider vinegar solution paired with motion was not affected by lesioning of the area postrema, but these taste aversions extinguished more slowly in lesioned rats than in sham-operates or intact controls. Results are discussed in terms of proposed humoral factors which may induce motion sickness and in light of recent data on the role of the area postrema in similar measures in species possessing the complete emetic reflex.