Multiple Conclusion Rules in Logics with the Disjunction Property

We prove that for the intermediate logics with the disjunction property any basis of admissible rules can be reduced to a basis of admissible m-rules (multiple-conclusion rules), and every basis of admissible m-rules can be reduced to a basis of admissible rules. These results can be generalized to a broad class of logics including positive logic and its extensions, Johansson logic, normal extensions of S4, n-transitive logics and intuitionistic modal logics

On the Concept of a Notational Variant

In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these accounts use, however, is too strong, as the standard translation from modal logic to first-order logic is not compositional in this sense. In light of this, we will explore a weaker version of this notion that we will call schematicity and show that there is no schematic translation either from first-order logic to propositional logic or from intuitionistic logic to classical logic

Short range electromagnetic interface using 0.35 m CMOS blocks for temperature monitoring in isolated areas

Introduction: Infra-red (IR) and visible light (VL) based systems developed for transmission of information about physical quantities (e.g. humidity, temperature) out from closed areas, cannot be effectively employed in case of specific conditions in a targeted environment (because of fog or vapor for example). Objectives: In this work, we introduce a concept of wireless short-range transmitter and receiver to sense physical quantities, for instance temperature, with slow variation. The proposed concept is able to transmit analog-based information from isolated environments (e.g. aquariums or environments for plant growing) with high immunity against vapor and fog that limits standard optical (laser, IR band) methods of communication. Methods: In this work, a new concept of short range radiofrequency (RF) communication device consisting of transmitting and receiving parts build from active devices fabricated in 0.35 m I3T25 3.3 V CMOS process and ferrite antennas is selected. RF part uses medium-wave propagation within 10 mm distance at frequency 700 kHz. Such an approach offers minimal path loss of the radiated energy of a signal and low-gain amplification required for restoration of similar levels as available at the transmitting side. Results: The processing of base-band signals of simple (sine wave) and complex (electrocardiogram) character was verified experimentally through the system. Application example of temperature monitoring in a closed environment, based on a temperature sensor (thermistor), verifies operationability in temperature range from 10 °C up to 50 °C. Conclusion: Compared to state-of-the-art solution, the presented concept has several advantages, for instance: less complexity; using of simpler type of modulation and demodulation; lower power consumption and significantly reduced issues caused by an environment with special transmission conditions (e.g. fog and vapor). The obtained results are in good agreement with expectations. Among others, the presented system brings beneficial performances for similar applications targeting on monitoring of low-frequency or slowly varying signal

Anticlockwise metamorphic pressure–temperature paths and nappe stacking in the Reisa Nappe Complex in the Scandinavian Caledonides, northern Norway: evidence for weakening of lower continental crust before and during continental collision

This study investigates the tectonostratigraphy and metamorphic and tectonic evolution of the Caledonian Reisa Nappe Complex (RNC; from bottom to top: Vaddas, Kåfjord, and Nordmannvik nappes) in northern Troms, Norway. Structural data, phase equilibrium modelling, and U-Pb zircon and titanite geochronology are used to constrain the timing and pressure–temperature (P–T) conditions of deformation and metamorphism during nappe stacking that facilitated crustal thickening during continental collision. Five samples taken from different parts of the RNC reveal an anticlockwise P–T path attributed to the effects of early Silurian heating (D1) followed by thrusting (D2). At ca. 439&thinsp;Ma during D1 the Nordmannvik Nappe reached the highest metamorphic conditions at ca. 780&thinsp;∘C and ∼9–11&thinsp;kbar inducing kyanite-grade partial melting. At the same time the Kåfjord Nappe was at higher, colder, levels of the crust ca. 600&thinsp;∘C, 6–7&thinsp;kbar and the Vaddas Nappe was intruded by gabbro at &gt;&thinsp;650&thinsp;∘C and ca. 6–9&thinsp;kbar. The subsequent D2 shearing occurred at increasing pressure and decreasing temperatures ca. 700&thinsp;∘C and 9–11&thinsp;kbar in the partially molten Nordmannvik Nappe, ca. 600&thinsp;∘C and 9–10&thinsp;kbar in the Kåfjord Nappe, and ca. 640&thinsp;∘C and 12–13&thinsp;kbar in the Vaddas Nappe. Multistage titanite growth in the Nordmannvik Nappe records this evolution through D1 and D2 between ca. 440 and 427&thinsp;Ma, while titanite growth along the lower RNC boundary records D2 shearing at 432±6&thinsp;Ma. It emerges that early Silurian heating (ca. 440&thinsp;Ma) probably resulted from large-scale magma underplating and initiated partial melting that weakened the lower crust, which facilitated dismembering of the crust into individual thrust slices (nappe units). This tectonic style contrasts with subduction of mechanically strong continental crust to great depths as seen in, for example, the Western Gneiss Region further south.</p

Admissible Bases Via Stable Canonical Rules

We establish the dichotomy property for stable canonical multi-conclusion rules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics

The complexity of theorem proving in autoepistemic logic

Autoepistemic logic is one of the most successful formalisms for nonmonotonic reasoning. In this paper we provide a proof-theoretic analysis of sequent calculi for credulous and sceptical reasoning in propositional autoepistemic logic, introduced by Bonatti and Olivetti [5]. We show that the calculus for credulous reasoning obeys almost the same bounds on the proof size as Gentzen's system LK. Hence proving lower bounds for credulous reasoning will be as hard as proving lower bounds for LK. This contrasts with the situation in sceptical autoepistemic reasoning where we obtain an exponential lower bound to the proof length in Bonatti and Olivetti's calculus

Proof Complexity of Non-classical Logics.

Proof complexity is an interdisciplinary area of research utilizing techniques from logic, complexity, and combinatorics towards the main aim of understanding the complexity of theorem proving procedures. Traditionally, propositional proofs have been the main object of investigation in proof complexity. Due their richer expressivity and numerous applications within computer science, also non-classical logics have been intensively studied from a proof complexity perspective in the last decade, and a number of impressive results have been obtained. In this paper we give the rst survey of this eld concentrating on recent developments in proof complexity of non-classical logics

Proof complexity of propositional default logic

Default logic is one of the most popular and successful formalisms for non-monotonic reasoning. In 2002, Bonatti and Olivetti introduced several sequent calculi for credulous and skeptical reasoning in propositional default logic. In this paper we examine these calculi from a proof-complexity perspective. In particular, we show that the calculus for credulous reasoning obeys almost the same bounds on the proof size as Gentzen’s system LK. Hence proving lower bounds for credulous reasoning will be as hard as proving lower bounds for LK. On the other hand, we show an exponential lower bound to the proof size in Bonatti and Olivetti’s enhanced calculus for skeptical default reasoning