Effects of a variable-ratio conditioning history on sensitivity to fixed-interval contingencies in rats.

We investigated the possibility that human-like fixed-interval performances would appear in rats given a variable-ratio history (Wanchisen, Tatham, & Mooney, 1989). Nine rats were trained under single or compound variable-ratio schedules and then under a fixed-interval 30-s schedule. The histories produced high fixed-interval rates that declined slowly over 90 sessions; differences as a function of the particular history were absent. Nine control animals given only fixed-interval training responded at lower levels initially, but rates increased with training. Despite differences in absolute rates, rates within the intervals and postreinforcement pauses indicated equivalent development of the accelerated response patterns suggestive of sensitivity to fixed-interval contingencies. The finding that the histories elevated rates without retarding development of differentiated patterns suggests that the effective response unit was a burst of several lever presses and that the fixed-interval contingencies acted on these units in the same way as for single responses. Regardless of history, the rats did not manifest the persistent, undifferentiated responding reported for humans under comparable schedules. We concluded that the shortcomings of animal models of human fixed-interval performances cannot be easily remedied by including a variable-ratio conditioning history within the model.     

Biasing the pacemaker in the behavioral theory of timing

In the behavioral theory of timing, pacemaker rate is determined by overall rate of reinforcement. A two-alternative free-operant psychophysical procedure was employed to investigate whether pacemaker period was also sensitive to the differential rate of reinforcement. Responding on a left key during the first 25 s and on a right key during the second 25 s of a 50-s trial was reinforced at variable intervals, and variable-interval schedule values during the two halves of the trials were varied systematically. Responding on the right key during the first 25 s and on the left key during the second 25 s was not reinforced. Estimates of pacemaker period were derived from fits of a function predicted by the behavioral theory of timing to right-key response proportions in consecutive 5-s bins of the 50-s trial. Estimates of pacemaker period were shortest when the differential reinforcer rate most strongly favored right-key responses, and were longest when the differential reinforcer rate most strongly favored left-key responses. The results were consistent with the conclusion that pacemaker rate is influenced by relative reinforcer rate.     

The logics of orthoalgebras

The notion of unsharp orthoalgebra is introduced and it is proved that the category of unsharp orthoalgebras is isomorphic to the category of D-posets. A completeness theorem for some partial logics based on unsharp orthoalgebras, orthoalgebras and orthomodular posets is proved.     

Temporal discrimination learning of operant feeding in goldfish (Carassius auratus)

Operant temporal discrimination learning was investigated in goldfish. In the first experiment, there was a fixed daily change in illumination. Eight subjects were trained to operate a lever that reinforced each press with food. The period during which responses were reinforced was then progressively reduced until it was 1 hr in every 24. The final 1-hr feeding schedule was maintained over 4 weeks. The feeding period commenced at the same time each day throughout. The food dispensers were then made inactive, and a period of extinction ensued for 6 days. The pattern of responding suggested that the fish were able to exhibit temporal discrimination in anticipation of feeding time. This pattern of responding persisted for a limited number of days during the extinction procedure. The second experiment produced evidence that operant temporal discrimination could develop under continuous illumination.     

Undecidability and intuitionistic incompleteness

Let S be a deductive system such that S-derivability (s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and s, it follows constructively that the K-completeness of s implies MP(S), a form of Markov's Principle. If s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when s is many-one complete, MP(S) implies the usual Markov's Principle MP.An immediate corollary is that the Tarski, Beth and Kripke weak completeness theorems for the negative fragment of intuitionistic predicate logic are unobtainable in HAS. Second, each of these: weak completeness for classical predicate logic, weak completeness for the negative fragment of intuitionistic predicate logic and strong completeness for sentential logic implics MP. Beth and Kripke completeness for intuitionistic predicate or sentential logic also entail MP.These results give extensions of the theorem of Gödel and Kreisel (in [4]) that completeness for pure intuitionistic predicate logic requires MP. The assumptions of Gödel and Kreisel's original proof included the Axiom of Dependent Choice and Herbrand's Theorem, no use of which is explicit in the present article.     

On maximal intermediate predicate constructive logics

We extend to the predicate frame a previous characterization of the maximal intermediate propositional constructive logics. This provides a technique to get maximal intermediate predicate constructive logics starting from suitable sets of classically valid predicate formulae we call maximal nonstandard predicate constructive logics. As an example of this technique, we exhibit two maximal intermediate predicate constructive logics, yet leaving open the problem of stating whether the two logics are distinct. Further properties of these logics will be also investigated.Presented by H. Ono     

Contrary-to-duty obligations

We investigate under what conditions contrary-to-duty (CTD) structures lacking temporal and action elements can be given a coherent reading. We argue, contrary to some recent proposals, that CTD is not an instance of defeasible reasoning, and that methods of nonmonotonic logics are inadequate since they are unable to distinguish between defeasibility and violation of primary obligations. We propose a semantic framework based on the idea that primary and CTD obligations are obligations of different kinds: a CTD obligation pertains to, or pre-supposes, a certain context in which a primary obligation is already violated. This framework is presented initially as an extension of Standard Deontic Logic (SDL), a normal modal logic of type KD, and is illustrated by application to a series of examples. The concluding section is concerned with some resemblances between CTD and defeasible reasoning. We show first that the SDL-based framework contains a flaw and must be adjusted. A discussion of possible adjustments, including an alternative treatment in terms of a preference-based semantics, reveals difficulties that are reminiscent of problems in defeasible reasoning and intensional accounts of defeasible conditionals.