Completeness in Hybrid Type Theory

We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret \(@_i\) in propositional and first-order hybrid logic. This means: interpret \(@_i\alpha _a\) , where \(\alpha _a\) is an expression of any type \(a\) , as an expression of type \(a\) that rigidly returns the value that \(\alpha_a\) receives at the i-world. The axiomatization and completeness proofs are generalizations of those found in propositional and first-order hybrid logic, and (as is usual inhybrid logic) we automatically obtain a wide range of completeness results for stronger logics and languages. Our approach is deliberately low-tech. We don’t, for example, make use of Montague’s intensional type s, or Fitting-style intensional models; we build, as simply as we can, hybrid logicover Henkin’s logic.     

Incubation of conditional suppression is an associatively-based phenomenon

Ten rats were deprived of water and trained to lick a tube for saccharin reinforcement. In each of the two sessions that followed, the rats received six contiguous pairings of a 30-second illumination of the houselight and a 0.75 second, 0.10 mA electric shock while licking. No sign of conditioning was observed during the first experimental session, but profound conditioning was observed on the first and subsequent trials of the second conditioning session. No comparable change in the rate of licking was observed in groups of rats that received only presentations of the visual stimulus, only presentations of the electric shock, or random presentation of the visual stimulus and electric shock during the first conditioning session. These data establish that the incubation of conditional suppression is an associative phenomenon.     

The encoding of perceptual information in the organization of individual stimulus patterns

Two experiments compared the effectiveness of variable physical dimensions and relationships among the components of individual stimulus patterns as means for encoding perceptual information. Four different codes were constructed in which letters (A through P) were represented by redundant combinations of the shape and brightness of the four component forms in each stimulus pattern. Three of the codes differed in terms of the physical variables that were redundant, and a fourth code was designed to simplify the relationships within individual stimulus patterns. Ss were asked to identify each pattern by naming its letter label as rapidly as possible. Differences in the speed of identification between codes and between individual patterns within codes indicated that perceptual information was effectively encoded by the organization of relationships within individual stimulus patterns. The representation of stimulation in terms of relationships among components has several implications for models of human information processing.     

Physicians' values and their career stage

Professional values of 241 practicing physicians were determined from factor analyzing their responses to 25 questionnaire items dealing with an ideal medical school in their vicinity. The seven factors (values)—(1) Academic, (2) Professional Separatism, (3) Support, (4) Social Welfare, (5) Research/Specialization, (6) Status/ Prestige, and (7) Convenience—were examined for their relationship to background characteristics (e.g., training) and practice (e.g., specialty). Few differences were found. However, when values were analyzed by age and career stage, significant fluctuations were found. Levinson's adult development theory was able to account for a sizeable portion of the observed variations. Practical and theoretical consequences are discussed in connection with physician stress at critical career stages.     

A model of pavlovian conditioning: Variations in representations of the unconditional stimulus

We present a model of Pavlovian excitatory conditioning in which associative strength and malleable central representations of unconditional stimuli determine the strength of conditional responding. Presentation of a conditioned stimulus acts through an experientially determined associative bond to activate a representation of the unconditional stimulus. The activation of the representation produces a conditioned response. A striking feature of the model is its ability to describe changes in conditioned response magnitude in terms of alterations of representations of the unconditional stimulus. Another is its acknowledgement of the capacity of associative bonds to survive behavioral extinction. The model describes much of the data reported from excitatory conditioning experiments and predicts counterintuitive phenomena. This work was supported by Natural Sciences and Engineering Research Council grant #U0262 awarded to the first author.     

Pure Extensions, Proof Rules, and Hybrid Axiomatics

In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language (a decidable system with the same complexity as orthodox propositional modal logic) to the strong Priorean language (which offers full first-order expressivity).We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it is possible to define base logics which extend automatically to a wide variety of frame classes and to prove completeness using the Henkin method. In the weaker languages, this requires the use of non-orthodox rules. We discuss these rules in detail and prove non-eliminability and eliminability results. We also show how another type of rule, which reflects the structure of the strong Priorean language, can be employed to give an even wider coverage of frame classes. We show that this deductive apparatus gets progressively simpler as we work our way up the expressivity hierarchy, and conclude the paper by showing that the approach transfers to first-order hybrid logic.A preliminary version of this paper was presented at the fifth conference on Advances in Modal Logic (AiML 2004) in Manchester. We would like to thank Maarten Marx for his comments on an early draft and Agnieszka Kisielewska for help with the proof reading.Special Issue Ways of Worlds II. On Possible Worlds and Related Notions Edited by Vincent F. Hendricks and Stig Andur Pedersen