Gentzen-Type Methods for Bilattice Negation

A general Gentzen-style framework for handling both bilattice (or strong) negation and usual negation is introduced based on the characterization of negation by a modal-like operator. This framework is regarded as an extension, generalization or re- finement of not only bilattice logics and logics with strong negation, but also traditional logics including classical logic LK, classical modal logic S4 and classical linear logic CL. Cut-elimination theorems are proved for a variety of proposed sequent calculi including CLS (a conservative extension of CL) and CLS_cw (a conservative extension of some bilattice logics, LK and S4). Completeness theorems are given for these calculi with respect to phase semantics, for SLK (a conservative extension and fragment of LK and CLS_cw, respectively) with respect to a classical-like semantics, and for SS4 (a conservative extension and fragment of S4 and CLScw, respectively) with respect to a Kripke-type semantics. The proposed framework allows for an embedding of the proposed calculi into LK, S4 and CL.     

Completeness and Cut-Elimination for First-Order Ideal Paraconsistent Four-Valued Logic

Studia Logica - In this study, we prove the completeness and cut-elimination theorems for a first-order extension F4CC of Arieli, Avron, and Zamansky’s ideal paraconsistent four-valued logic...     

Tactile perception of nonpainful unpleasantness in relation to perceived roughness: effects of inter-element spacing and speed of relative motion of rigid 2-D raised-dot patterns at two body loci

Rigid surfaces consisting of spatially jittered 2-D raised-dot patterns with different inter-element spacings were moved back and forth across the skin at three different speeds (10-fold range). Within each psychophysical experiment, participants numerically estimated the perceived magnitude of either unpleasantness (nonpainful) or roughness of 2-D raised-dot surfaces applied to two stationary body sites (experiment 1: fingers; experiment 2: forearm). The psychophysical functions for the two types of perceptual judgment were highly similar at both body loci; more specifically, the perceived magnitude of unpleasantness and roughness both increased monotonically as a power function of increasing inter-element spacing, with the rate of growth declining at the upper end of the continuum. These results suggest that inter-element spacing is a critical determinant of the perceived magnitude of unpleasantness (nonpainful), as well as of roughness. Each perceptual judgment also increased as a function of increasing relative speed at both body loci. However, the magnitude of this effect was significantly greater for perceived unpleasantness than for perceived roughness; conversely, the speed effect was significantly greater on the forearm than on the fingers. Several possible explanations for these findings are considered.     

Normal Modal Substructural Logics with Strong Negation

We introduce modal propositional substructural logics with strong negation, and prove the completeness theorems (with respect to Kripke models) for these logics.     

Correction to: Kripke-Completeness and Cut-elimination Theorems for Intuitionistic Paradefinite Logics With and Without Quasi-Explosion

Journal of Philosophical Logic - The original version of this article unfortunately contains several errors introduced by the typesetter during the publishing process. It has been corrected.     

Kripke-Completeness and Cut-elimination Theorems for Intuitionistic Paradefinite Logics With and Without Quasi-Explosion

Journal of Philosophical Logic - Two intuitionistic paradefinite logics N4C and N4C+ are introduced as Gentzen-type sequent calculi. These logics are regarded as a combination of Nelson’s...     

Suppression of brain activity related to a car-following task with an auditory task: An fMRI study

Driving a car in daily life involves multiple tasks. One important task for safe driving is car-following, the interference of which causes rear-end collisions: the most common type of car accident. Recent reports have described that car-following is hindered even by hands-free mobile telephones. We conducted functional MRI with 18 normal volunteers to investigate brain activity changes that occur during a car-following task with a concurrent auditory task. Participants performed three tasks: a driving task, an auditory task, and a dual task in an fMRI run. During the driving task, participants use a joystick to control their vehicle speed in a driving simulator to maintain a constant distance from a leading car, which moves at varying speed. Language trials and tone discrimination trials are presented during the auditory task. Car-following performance was worse during the dual task than during the single-driving task, showing positive correlation with brain activity in the bilateral lateral occipital complex and the right inferior parietal lobule. In the medial prefrontal cortex and left superior occipital gyrus, the brain activity of the dual task condition was less than that in the single-driving task condition. These results suggest that the decline of brain activity in these regions may induce car-following performance deterioration.     

Hemodynamic and electrophysiological relationship involved in human face processing: evidence from a combined fMRI-ERP study

Functional magnetic resonance imaging (fMRI) and event-related potential (ERP) experiments were conducted in the same group of subjects and with an identical task paradigm to investigate a possible relationship between hemodynamic and electrophysiological responses within the brain. The subjects were instructed to judge whether visually presented stimuli were faces or houses and then press the corresponding button. Functional MRI identified face- and house-related regions in the lateral and medial part of the fusiform gyrus, respectively, while ERP showed significantly greater N170 negativity for face than for house stimuli in the temporo-occipital electrodes. Correlation analysis between the BOLD signal in the fusiform gyrus and ERP parameters demonstrated a close relationship between the signal and both latency and amplitude of N170 across the subjects. These correlations may indicate that the variation in cognitive demand and hemodynamic responses during the face/house discrimination task is coupled with the variation of N170 peak latency/amplitude across the subjects. Thus, integrative analysis of spatial and temporal information obtained from the two experimental modalities may help in studying neural correlates involved in a particular cognitive task.     

Combining linear-time temporal logic with constructiveness and paraconsistency

It is known that linear-time temporal logic (LTL), which is an extension of classical logic, is useful for expressing temporal reasoning as investigated in computer science. In this paper, two constructive and bounded versions of LTL, which are extensions of intuitionistic logic or Nelson's paraconsistent logic, are introduced as Gentzen-type sequent calculi. These logics, $\mathrm{IB}[l]$ and $\mathrm{PB}[l]$, are intended to provide a useful theoretical basis for representing not only temporal (linear-time), but also constructive, and paraconsistent (inconsistency-tolerant) reasoning. The time domain of the proposed logics is bounded by a fixed positive integer. Despite the restriction on the time domain, the logics can derive almost all the typical temporal axioms of LTL. As a merit of bounding time, faithful embeddings into intuitionistic logic and Nelson's paraconsistent logic are shown for $\mathrm{IB}[l]$ and $\mathrm{PB}[l]$, respectively. Completeness (with respect to Kripke semantics), cut–elimination, normalization (with respect to natural deduction), and decidability theorems for the newly defined logics are proved as the main results of this paper. Moreover, we present sound and complete display calculi for $\mathrm{IB}[l]$ and $\mathrm{PB}[l]$.In [P. Maier, Intuitionistic LTL and a new characterization of safety and liveness, in: Proceedings of Computer Science Logic 2004, in: Lecture Notes in Computer Science, vol. 3210, Springer-Verlag, Berlin, 2004, pp. 295–309] it has been emphasized that intuitionistic linear-time logic (ILTL) admits an elegant characterization of safety and liveness properties. The system ILTL, however, has been presented only in an algebraic setting. The present paper is the first semantical and proof-theoretical study of bounded constructive linear-time temporal logics containing either intuitionistic or strong negation.