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

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

Thermal and mechanical evolution of collisional and accretionary orogens: a volume in honour of Karel Schulmann—an introduction

International audienceProfessor Karel Schulmann (Fig. 1) is a scientific leader in the domain of structural geology, tectonics of collisional and accretionary systems and geodynamic processes in general. His publication record is impressive both in terms of quality and quantity (190 refereed papers and over 6200 citations). Karel Schulmann has basically founded the modern basement geology community in the Czech Republic and greatly contributed to the development of this discipline in France. This volume is an outcome of a conference in honour of Karel Schulmann’s 60th birthday entitled Thermal and mechanical evolution of collisional and accretionary orogens held in Třešť, Czech Republic from August 31st to September 2nd, 2018. This conference featured over 50 contributions from colleagues, former students and friends all around the world and 17 selected contributions are presented in this volume