Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics

We present two embeddings of infinite-valued Lukasiewicz logic L into Meyer and Slaney's abelian logic A, the logic of lattice-ordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding systems for L. These include: hypersequent calculi for A and L and terminating versions of these calculi; labelled single sequent calculi for A and L of complexity co-NP; unlabelled single sequent calculi for A and L.Comment: 35 pages, 1 figur

Goal-directed proof theory

This report is the draft of a book about goal directed proof theoretical formulations of non-classical logics. It evolved from a response to the existence of two camps in the applied logic (computer science/artificial intelligence) community. There are those members who believe that the new non-classical logics are the most important ones for applications and that classical logic itself is now no longer the main workhorse of applied logic, and there are those who maintain that classical logic is the only logic worth considering and that within classical logic the Horn clause fragment is the most important one. The book presents a uniform Prolog-like formulation of the landscape of classical and non-classical logics, done in such away that the distinctions and movements from one logic to another seem simple and natural; and within it classical logic becomes just one among many. This should please the non-classical logic camp. It will also please the classical logic camp since the goal directed formulation makes it all look like an algorithmic extension of Logic Programming. The approach also seems to provide very good compuational complexity bounds across its landscape

A Behavioral Approach to Treatment and Assessment of People with Disorders of Consciousness: The Response-contingent Stimulation Strategy

Response-contingent stimulation is a behavioral strategy used to improve the situation of patients with disorders of consciousness. Such strategy involves the presentation of brief periods (e.g., 10 to 15 s) of stimulation considered preferred by the patients, contingent on (immediately after) the emission of specific patients' responses. The aim is to help the patients learn the link between their responding and the preferred stimulation and thus learn to use their responding to access the stimulation in a self-determined/independent manner. Achieving these goals is considered important for the patients' recovery process and thus the response-contingent stimulation strategy that promotes such an achievement can be considered a valuable treatment approach. The same strategy combined with the use of periods of non-contingent stimulation (i.e., stimulation delivered independent of responding) may also serve as an assessment supplement with patients with apparent unresponsive wakefulness. The patients' increase in responding during the response-contingent stimulation and decline in responding during the non-contingent stimulation could be taken as a sign of discrimination between conditions, and possibly a sign of awareness of the immediate environmental situation, compatible with a diagnosis of minimally conscious state. This paper analyzes a number of studies aimed at using the response-contingent stimulation as a treatment strategy and a number of studies aimed at combining response-contingent stimulation with non-contingent stimulation for treatment and assessment purposes. The results of the studies are discussed in terms of the effectiveness, accessibility and affordability of the strategy. The need for new research (i.e., replication studies) is also pointed out

Generic Modal Cut Elimination Applied to Conditional Logics

We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies also to a wide variety of logics outside the realm of normal modal logic. We give extensive example instantiations of our framework to various conditional logics. For these, we obtain fully internalised calculi which are substantially simpler than those known in the literature, along with leaner proofs of cut elimination and complexity. In one case, conditional logic with modus ponens and conditional excluded middle, cut elimination and complexity were explicitly stated as open in the literature

Optimizing the magnon-phonon cooperativity in planar geometries

Optimizing the cooperativity between two distinct particles is an important feature of quantum information processing. Of particular interest is the coupling between spin and phonon, which allows for integrated long range communication between gates operating at GHz frequency. Using local light scattering, we show that, in magnetic planar geometries, this attribute can be tuned by adjusting the orientation and strength of an external magnetic field. The coupling strength is enhanced by about a factor of 2 for the out-of-plane magnetized geometry where the Kittel mode is coupled to circularly polarized phonons, compared to the in-plane one where it couples to linearly polarized phonons. We also show that the overlap between magnon and phonon is maximized by matching the Kittel frequency with an acoustic resonance that satisfies the half-wave plate condition across the magnetic film thickness. Taking the frequency dependence of the damping into account, a maximum cooperativity of about 6 is reached in garnets for the normal configuration near 5.5 GHz