The semantic view of theories and higher-order languages

Several philosophers of science construe models of scientific theories as set-theoretic structures. Some of them moreover claim that models should not be construed as structures in the sense of model theory because the latter are language-dependent. I argue that if we are ready to construe models as set-theoretic structures (strict semantic view), we could equally well construe them as model-theoretic structures of higher-order logic (liberal semantic view). I show that every family of set-theoretic structures has an associated language of higher-order logic and an up to signature isomorphism unique model-theoretic counterpart, which is able to serve the same purposes. This allows to carry over every syntactic criterion of equivalence for theories in the sense of the liberal semantic view to theories in the sense of the strict semantic view. Taken together, these results suggest that the recent dispute about the semantic view and its relation to the syntactic view can be resolved

Definable categorical equivalence

This article proposes to explicate theoretical equivalence by supplementing formal equivalence criteria with preservation conditions concerning interpretation. I argue that both the internal structure of models and choices of morphisms are aspects of formalisms that are relevant when it comes to their interpretation. Hence, a formal criterion suitable for being supplemented with preservation conditions concerning interpretation should take these two aspects into account. The two currently most important criteria—gener-alized definitional equivalence (Morita equivalence) and categorical equivalence—are not optimal in this respect. I put forward a criterion that takes both aspects into account: the criterion of definable categorical equivalence

The semantic view of theories and higher-order languages

Several philosophers of science construe models of scientific theories as set-theoretic structures. Some of them moreover claim that models should not be construed as structures in the sense of model theory because the latter are language-dependent. I argue that if we are ready to construe models as set-theoretic structures (strict semantic view), we could equally well construe them as model-theoretic structures of higher-order logic (liberal semantic view). I show that every family of set-theoretic structures has an associated language of higher-order logic and an up to signature isomorphism unique model-theoretic counterpart, which is able to serve the same purposes. This allows to carry over every syntactic criterion of equivalence for theories in the sense of the liberal semantic view to theories in the sense of the strict semantic view. Taken together, these results suggest that the recent dispute about the semantic view and its relation to the syntactic view can be resolved

Desflurane Selectively Suppresses Long-latency Cortical Neuronal Response to Flash in the Rat

Background—The effect of inhalational anesthetics on sensory-evoked unit activity in the cerebral cortex has been controversial. Desflurane has desirable properties for in vivo neurophysiologic studies but its effect on cortical neuronal activity and neuronal responsiveness is not known. We studied the effect of desflurane on resting and visual evoked unit activity in rat visual cortex in vivo. Methods—Desflurane was administered to adult albino rats at steady-state concentrations at 2%, 4%, 6% and 8%. Flashes from a light emitting diode were delivered to the left eye at 5-second intervals. Extracellular unit activity within the right visual cortex was recorded using a 49-electrode array. Individual units were identified using principal components analysis. Results—At 2% desflurane 578 active units were found. Of these, 75% increased their firing rate in response to flash. Most responses contained early (0–100ms) and late (150–1000ms) components. With increasing desflurane concentration, the number of units active at baseline decreased (−13%), the number of early responding units increased (+31%), and number of late responding units decreased (−15%). Simultaneously, baseline firing rate decreased (−77%), the early response was unchanged, and the late response decreased (−60%). Conclusions—The results indicate that visual cortex neurons remain responsive to flash stimulation under desflurane anesthesia but the long-latency component of their response is attenuated in a concentration-dependent manner. Suppression of the long-latency response may be related to a loss of cortico-cortical feedback and loss of consciousness

Critical Changes in Cortical Neuronal Interactions in Anesthetized and Awake Rats

Background: Neuronal interactions are fundamental for information processing, cognition and consciousness. Anesthetics reduce spontaneous cortical activity; however, neuronal reactivity to sensory stimuli is often preserved or augmented. How sensory stimulus-related neuronal interactions change under anesthesia has not been elucidated. Here we investigated visual stimulus-related cortical neuronal interactions during stepwise emergence from desflurane anesthesia. Methods: Parallel spike trains were recorded with 64-contact extracellular microelectrode arrays from the primary visual cortex of chronically instrumented, unrestrained rats (N=6) at 8%, 6%, 4%, 2% desflurane anesthesia and wakefulness. Light flashes were delivered to the retina by transcranial illumination at 5-15s randomized intervals. Information theoretical indices, integration and interaction complexity, were calculated from the probability distribution of coincident spike patterns and used to quantify neuronal interactions before and after flash stimulation. Results: Integration and complexity showed significant negative associations with desflurane concentration (N=60). Flash stimulation increased integration and complexity at all anesthetic levels (N=60); the effect on complexity was reduced in wakefulness. During stepwise withdrawal of desflurane, the largest increase in integration (74%) and post-stimulus complexity (35%) occurred prior to reaching 4% desflurane concentration – a level associated with the recovery of consciousness according to the rats\u27 righting reflex. Conclusions: Neuronal interactions in the cerebral cortex are augmented during emergence from anesthesia. Visual flash stimuli enhance neuronal interactions in both wakefulness and anesthesia; the increase in interaction complexity is attenuated as post-stimulus complexity reaches plateau. The critical changes in cortical neuronal interactions occur during transition to consciousness

Monosynaptic Functional Connectivity in Cerebral Cortex During Wakefulness and Under Graded Levels of Anesthesia

The balance between excitation and inhibition is considered to be of significant importance for neural computation and cognitive function. Excitatory and inhibitory functional connectivity in intact cortical neuronal networks in wakefulness and graded levels of anesthesia has not been systematically investigated. We compared monosynaptic excitatory and inhibitory spike transmission probabilities using pairwise cross-correlogram (CCG) analysis. Spikes were measured at 64 sites in the visual cortex of rats with chronically implanted microelectrode arrays during wakefulness and three levels of anesthesia produced by desflurane. Anesthesia decreased the number of active units, the number of functional connections, and the strength of excitatory connections. Connection probability (number of connections per number of active unit pairs) was unaffected until the deepest anesthesia level, at which a significant increase in the excitatory to inhibitory ratio of connection probabilities was observed. The results suggest that the excitatory–inhibitory balance is altered at an anesthetic depth associated with unconsciousness

Modeling Resting-State Functional Networks When the Cortex Falls Asleep: Local and Global Changes

The transition from wakefulness to sleep represents the most conspicuous change in behavior and the level of consciousness occurring in the healthy brain. It is accompanied by similarly conspicuous changes in neural dynamics, traditionally exemplified by the change from "desynchronized” electroencephalogram activity in wake to globally synchronized slow wave activity of early sleep. However, unit and local field recordings indicate that the transition is more gradual than it might appear: On one hand, local slow waves already appear during wake; on the other hand, slow sleep waves are only rarely global. Studies with functional magnetic resonance imaging also reveal changes in resting-state functional connectivity (FC) between wake and slow wave sleep. However, it remains unclear how resting-state networks may change during this transition period. Here, we employ large-scale modeling of the human cortico-cortical anatomical connectivity to evaluate changes in resting-state FC when the model "falls asleep” due to the progressive decrease in arousal-promoting neuromodulation. When cholinergic neuromodulation is parametrically decreased, local slow waves appear, while the overall organization of resting-state networks does not change. Furthermore, we show that these local slow waves are structured macroscopically in networks that resemble the resting-state networks. In contrast, when the neuromodulator decrease further to very low levels, slow waves become global and resting-state networks merge into a single undifferentiated, broadly synchronized networ

Quantum dynamical entropies for classical stochastic systems

We compare two proposals for the dynamical entropy of quantum deterministic systems (CNT and AFL) by studying their extensions to classical stochastic systems. We show that the natural measurement procedure leads to a simple explicit expression for the stochastic dynamical entropy with a clear information-theoretical interpretation. Finally, we compare our construction with other recent proposals.Comment: 15 page

The semantic view of theories and higher-order languages

Several philosophers of science construe models of scientifc theories as set-theoretic structures. Some of them moreover claim that models should not be construed as structures in the sense of model theory because the latter are language dependent. I argue that if we are ready to construe models as set-theoretic structures (strict semantic view), we could equally well construe them as model-theoretic structures of higher-order logic (liberal semantic view). I show that every family of set-theoretic structures has an associated language of higher-order logic and an up to signature isomorphism unique model-theoretic counterpart, which is able to serve the same purposes. This allows to carry over every syntactic criterion of equivalence for theories in the sense of the liberal semantic view to theories in the sense of the strict semantic view. Taken together, these results suggest that the recent dispute about the semantic view and its relation to the syntactic view can be resolved