Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

What is modal logic

Натрийуретические пептиды (НУП) являются важными биомаркерами в диагностике и определении прогноза у пациентов с сердечной недостаточностью (СН). Оценка динамики концентрации НУП (BNP, Nt -proBNP) может быть использована в качестве критерия успешности проводимой терапии. так, при достижении целевых уровней НУП можно прогнозировать благоприятный исход заболевания. В настоящее время лечение СН с учетом уровней НУП является частью рекомендаций по лечению СН (класс IIа) и улучшению ее исхода (класс IIб) в США, однако такой подход не используется в российских клиниках. Цель. Представить современный взгляд на возможность использования НУП для оценки эффективности проводимой терапии пациентов с СН. Ключевые слова: натрийуретические пептиды, сердечная недостаточность, оценка эффективности терапии.

Федеральное государственное бюджетное учреждение «Научно-исследовательский институт комплексных проблем сердечно-сосудистых заболеваний» Сибирского отделения Российской академии медицинских наук, Кемерово, Россия

Publisher Summary This chapter focuses on the concept of Galois connexions. The researches in algebraic linguistics have been performed in the frame of a particular Galois connexion, in which the objects are the words of a vocabulary, V, and the set of the properties is the set of the contexts that accept these words. Vocabulary V is, however, formed by a finite of words. The chapter highlights that if A is a generating kernel for the closed set φ ( X ), then the set formed by taking one element of every family contained in A is also a generator for φ ( X ). Such a generator is called the minimal generator of the set φ( X ) with respect to the kernel A . The chapter also discusses the properties of the operators G , ω , and φ .

On Galois Connexions

In the first section logics with an algebraic semantics are investigated. Section 2 is devoted to subdirect products of matrices. There, among others we give the matrix counterpart of a theorem of Jonsson from universal algebra. Some positive results concerning logics with, finite degrees of maximality are presented in Section 3.

Equivalential logics (II)

A projective unifier for a modal formula A, over a modal logic L, is a unifier σ for A (i.e. a substitution making A a theorem of L) such that the equivalence of σ with the identity map is the consequence of A. Each projective unifier is a most general unifier for A. Let L be a normal modal logic containing S4. We show that every unifiable formula has a projective unifier in L iff L contains S4.3. The syntactic proof is effective. As a corollary, we conclude that all normal modal logics L containing S4.3 are almost structurally complete, i.e. all (structural) admissible rules having unifiable premises are derivable in L. Moreover, L is (hereditarily) structurally complete iff L contains McKinsey axiom M .

Projective unification in modal logic

Structural completeness of Gödel's and Dummett's propositional calculi

Relational representation theorems are presented for general (i.e., non-distributive) lattices with the following types of negations: De Morgan, ortho, Heyting and pseudo-complement. The representation is built on Urquhart's representation for lattices where the associated relational structures are doubly ordered sets and the canonical frame of a lattice consists of its maximal disjoint filter-ideal pairs. For lattices with negation, the relational structures require an additional binary relation satisfying certain conditions which derive from the properties of the negation. In each case, these conditions are sufficient to ensure that the lattice with negation is embeddable into the complex algebra of its canonical frame.

Relational representation theorems for general lattices with negations

A b s t r a c t. Abstract. It is shown that substructural logics of kpotent BL-algebras and k-potent hoops have unitary unification (in fact, transparent unifiers) while Basic Fuzzy Logic, BL (the logic of BL-algebras), and ∞-valued Lukasiewicz logic (the logic of MV-algebras) do not have unitary unification. It follows that every k-potent substructural logic containing BL is structurally complete in the restricted sense, but Basic Logic itself is not.

Unification in some substructural logics of BL-algebras and hoops

In this work, an intuitionistic propositional logic with a Galois connection (IntGC) is introduced. In addition to the intuitionistic logic axioms and inference rule of modus ponens, the logic contains only two rules of inference mimicking the performance of Galois connections. Both Kripke-style and algebraic semantics are presented for IntGC, and IntGC is proved to be complete with respect to both of these semantics. We show that IntGC has the finite model property and is decidable, but Glivenko’s Theorem does not hold. Duality between algebraic and Kripke semantics is presented, and a representation theorem for Heyting algebras with Galois connections is proved. In addition, an application to rough L-valued sets is presented.

Wojciech Dzik

Papers

Projective unification in modal logic

Structural completeness of Gödel's and Dummett's propositional calculi

Relational representation theorems for general lattices with negations

Unification in some substructural logics of BL-algebras and hoops

Intuitionistic propositional logic with Galois connections