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

Invited Lectures.- Tableau Algorithms for Description Logics.- Modality and Databases.- Local Symmetries in Propositional Logic.- Comparison.- Design and Results of TANCS-2000 Non-classical (Modal) Systems Comparison.- Consistency Testing: The RACE Experience.- Benchmark Analysis with FaCT.- MSPASS: Modal Reasoning by Translation and First-Order Resolution.- TANCS-2000 Results for DLP.- Evaluating *SAT on TANCS 2000 Benchmarks.- Research Papers.- A Labelled Tableau Calculus for Nonmonotonic (Cumulative) Consequence Relations.- A Tableau System for Godel-Dummett Logic Based on a Hypersequent Calculus.- An Analytic Calculus for Quantified Propositional Godel Logic.- A Tableau Method for Inconsistency-Adaptive Logics.- A Tableau Calculus for Integrating First-Order and Elementary Set Theory Reasoning.- Hypertableau and Path-Hypertableau Calculi for some Families of Intermediate Logics.- Variants of First-Order Modal Logics.- Complexity of Simple Dependent Bimodal Logics.- Properties of Embeddings from Int to S4.- Term-Modal Logics.- A Subset-Matching Size-Bounded Cache for Satisfiability in Modal Logics.- Dual Intuitionistic Logic Revisited.- Model Sets in a Nonconstructive Logic of Partial Terms with Definite Descriptions.- Search Space Compression in Connection Tableau Calculi Using Disjunctive Constraints.- Matrix-Based Inductive Theorem Proving.- Monotonic Preorders for Free Variable Tableaux.- The Mosaic Method for Temporal Logics.- Sequent-Like Tableau Systems with the Analytic Superformula Property for the Modal Logics KB, KDB, K5, KD5.- A Tableau Calculus for Equilibrium Entailment.- Towards Tableau-Based Decision Procedures for Non-Well-Founded Fragments of Set Theory.- Tableau Calculus for Only Knowing and Knowing At Most.- A Tableau-Like Representation Framework for Efficient Proof Reconstruction.- The Semantic Tableaux Version of the Second Incompleteness Theorem Extends Almost to Robinson's Arithmetic Q.- System Descriptions.- Redundancy-Free Lemmatization in the Automated Model-Elimination Theorem Prover AI-SETHEO.- E-SETHEO: An Automated3 Theorem Prover.

Automated Reasoning with Analytic Tableaux and Related Methods: International Conference, TABLEAUX 2000 St Andrews, Scotland, UK, July 3-7, 2000 Proceedings

Equilibrium logic is a general purpose nonmonotonic reasoning formalism closely aligned with answer set programming (ASP). In particular it provides a logical foundation for ASP as well as an extension of the basic syntax of answer set programs. We present an overview of equilibrium logic and its main properties and uses.

Equilibrium logic

We investigate a peculiar intuitionistic modal logic, called Propositional Lax Logic (PLL), which has promising applications to the formal verification of computer hardware. The logic has emerged from an attempt to express correctness up to behavioural constraints?a central notion in hardware verification?as a logical modality. As a modal logic it is special since it features a single modal operator ? that has a flavour both of possibility and of necessity. In the paper we provide the motivation for PLL and present several technical results. We investigate some of its proof-theoretic properties, presenting a cut-elimination theorem for a standard Gentzen-style sequent presentation of the logic. We go on to define a new class of fallible two-frame Kripke models for PLL. These models are unusual since they feature worlds with inconsistent information; furthermore, the only frame condition imposed is that the ?-frame be a subrelation of the ?-frame. We give a natural translation of these models into Goldblatt's J-space models of PLL. Our completeness theorem for these models yields a Godel-style embedding of PLL into a classical bimodal theory of type (S4,S4) and underpins a simple proof of the finite model property. We proceed to prove soundness and completeness of several theories for specialized classes of models. We conclude with a brief exploration of two concrete and rather natural types of model from hardware verification for which the modality ? models correctness up to timing constraints. We obtain decidability of ?-free fragment of the logic of the first type of model, which coincides with the stable form of Maksimova's intermediate logicL?.

Propositional Lax Logic

The paper presents a one-pass tableau calculus PLTLT for the propositional linear time logic PLTL. The calculus is correct and complete and unlike in previous decision methods, there is no second phase that checks for the fulfillment of the so-called eventuality formulae. This second phase is performed locally and is incorporated into the rules of the calculus. Derivations in PLTLT are cyclic trees rather than cyclic graphs. When used as a basis for a decision procedure, it has the advantage that only one branch needs to be kept in memory at any one time. It may thus be a suitable starting point for the development of a parallel decision method for PLTL.

A New One-Pass Tableau Calculus for PLTL

Duplication-free tableau calculi and related cut-free sequent calculi for the interpolable propositional intermediate logics

Given an intermediate propositional logic L (obtained by adding to intuitionistic logic INT a single axiom-scheme), a pseudo tableau system for L can be given starting from any intuitionistic tableau system and adding a rule which allows to insert in any line of a proof table suitable T-signed instances of the axiom-scheme. In this paper we study some sufficient conditions from which, given a well formed formula H, the search for these instances can be restricted to a suitable finite set of formulae related to H. We illustrate our techniques by means of some known logics, namely, the logic D of Dummett, the logics PR k (k≥1) of Nagata, the logics FIN m (m≥1), the logics G n (n≥1) of Gabbay and de Jongh, and the logic KP of Kreisel and Putnam

Generalized Tableau Systems for Intemediate Propositional Logics

https://boa.unimib.it/retrieve/handle/10281/310/5005/optimization_techniques_propositional_intuitionistic_logic.pdf

Optimization techniques for propositional intuitionistic logic and their implementation

Nous presentons un algorithme pour la reconnaissance des langages rationnels de traces qui a une complexite en temps au plus proportionnelle au nombre de prefixes de la trace d'entree. Dans le pire cas, il a un comportement en O (n n ) en temps et en O (n α-1 ) en espace, ou α est la taille de la clique maximale de l'alphabet d independance; en moyenne il a un comportement en O (n k ) en temps ou k est le nombre de composantes connexes de l'alphabet de dependance. Cet algorithme repose sur une technique de programmation dynamique qui peut aussi etre appliquee a la reconnaissance de langages libres de contexte de traces, Nous presentons une extension de l'algorithme classique de CYK qui travaille en temps O (n 3α ) et en espace O (n 2α ) dans le pire cas et en temps O (n 3k ) et en espace O (n 2k ) en moyenne.

/pdf/analysis-of-algorithms-for-the-recognition-of-rational-and-2iuqqbflfc.pdf

Analysis of algorithms for the recognition of rational and context-free trace languages

In this paper we propose a method for program synthesis from constructive proofs based on a particular proof strategy, we call dischargeable set construction. This proof-strategy allows to build proofs in which active patterns (sequences of application of rules with proper computational content) can be distinguished from correctness patterns (concerning correctness properties of the algorithm implicitly contained in the proof). The synthesis method associates with every active pattern of the proof a program schema (in an imperative language) translating only the computational content of the proof. One of the main features of our method is that it can be applied to a variety of theories formalizing ADT's and classes of ADT's. Here we will discuss the method and the computational content of some principles of particular interest in the context of some classes of ADT's.

Alessandro Avellone

Papers

Duplication-free tableau calculi and related cut-free sequent calculi for the interpolable propositional intermediate logics

Generalized Tableau Systems for Intemediate Propositional Logics

Optimization techniques for propositional intuitionistic logic and their implementation

Analysis of algorithms for the recognition of rational and context-free trace languages

Synthesis of Programs in Abstract Data Types