Long-range transport of Saharan dust to northern Europe: The 11-16 October 2001 outbreak observed with EARLINET

The spread of mineral particles over southwestern, western, and central Europeresulting from a strong Saharan dust outbreak in October 2001 was observed at10 stations of the European Aerosol Research Lidar Network (EARLINET). For the firsttime, an optically dense desert dust plume over Europe was characterized coherentlywith high vertical resolution on a continental scale. The main layer was located abovethe boundary layer (above 1-km height above sea level (asl)) up to 3–5-km height, andtraces of dust particles reached heights of 7–8 km. The particle optical depth typicallyranged from 0.1 to 0.5 above 1-km height asl at the wavelength of 532 nm, andmaximum values close to 0.8 were found over northern Germany. The lidar observationsare in qualitative agreement with values of optical depth derived from Total OzoneMapping Spectrometer (TOMS) data. Ten-day backward trajectories clearly indicated theSahara as the source region of the particles and revealed that the dust layer observed,e.g., over Belsk, Poland, crossed the EARLINET site Aberystwyth, UK, and southernScandinavia 24–48 hours before. Lidar-derived particle depolarization ratios,backscatter- and extinction-related A ° ngstro¨m exponents, and extinction-to-backscatterratios mainly ranged from 15 to 25%, 0.5 to 0.5, and 40–80 sr, respectively, within thelofted dust plumes. A few atmospheric model calculations are presented showing the dustconcentration over Europe. The simulations were found to be consistent with thenetwork observations.

On Arbitrary Selection Strategies for Basic Superposition

For first-order Horn clauses without equality, resolution is complete with an arbitrary selection of a single literal in each clause [dN 96]. Here we extend this result to the case of clauses with equality for superposition-based inference systems. Our result is a generalization of the result given in [BG 01]. We answer their question about the completeness of a superposition-based system for general clauses with an arbitrary selection strategy, provided there exists a refutation without applications of the factoring inference rule.

Monodic temporal resolution

Until recently, First-Order Temporal Logic (FOTL) has been only partially understood. While it is well known that the full logic has no finite axiomatisation, a more detailed analysis of fragments of the logic was not previously available. However, a breakthrough by Hodkinson et al., identifying a finitely axiomatisable fragment, termed the monodic fragment, has led to improved understanding of FOTL. Yet, in order to utilise these theoretical advances, it is important to have appropriate proof techniques for this monodic fragment.In this paper, we modify and extend the clausal temporal resolution technique, originally developed for propositional temporal logics, to enable its use in such monodic fragments. We develop a specific normal form for monodic formulae in FOTL, and provide a complete resolution calculus for formulae in this form. Not only is this clausal resolution technique useful as a practical proof technique for certain monodic classes, but the use of this approach provides us with increased understanding of the monodic fragment. In particular, we here show how several features of monodic FOTL can be established as corollaries of the completeness result for the clausal temporal resolution method. These include definitions of new decidable monodic classes, simplification of existing monodic classes by reductions, and completeness of clausal temporal resolution in the case of monodic logics with expanding domains, a case with much significance in both theory and practice.

Regular Derivations in Basic Superposition-Based Calculi

We prove the completeness of the regular strategy of derivations for superposition-based calculi. The regular strategy was pioneered by Kanger in [Kan63], who proposed that all equality inferences take place before all other steps in the proof. We show that the strategy is complete with the elimination of tautologies. The implication of our result is the completeness of non-standard selection functions by which in non-relational clauses only equality literals (and all of them) are selected.

Mechanising first-order temporal resolution

First-order temporal logic is a concise and powerful notation, with many potential applications in both Computer Science and Artificial Intelligence. While the full logic is highly complex, recent work on monodic first-order temporal logics has identified important enumerable and even decidable fragments. Although a complete and correct resolution-style calculus has already been suggested for this specific fragment, this calculus involves constructions too complex to be of practical value. In this paper, we develop a machine-oriented clausal resolution method which features radically simplified proof search. We first define a normal form for monodic formulae and then introduce a novel resolution calculus that can be applied to formulae in this normal form. By careful encoding, parts of the calculus can be implemented using classical first-order resolution and can, thus, be efficiently implemented. We prove correctness and completeness results for the calculus and illustrate it on a comprehensive example. An implementation of the method is briefly discussed.

Monodic Temporal Resolution

First-order temporal logic is a coincise and powerful notation, with many potential applications in both Computer Science and Artificial Intelligence. While the full logic is highly complex, recent work on monodic first-order temporal logics have identified important enumerable and even decidable fragments. In this paper we present the first resolution-based calculus for monodic first-order temporal logic. Although the main focus of the paper is on establishing completeness result, we also consider implementation issues and define a basic loop-search algorithm that may be used to guide the temporal resolution system.

Handling Equality in Monodic Temporal Resolution

First-order temporal logic is a concise and powerful notation, with many potential applications in both Computer Science and Artificial Intelligence. While the full logic is highly complex, recent work on monodic first-order temporal logics has identified important enumerable and even decidable fragments including the guarded fragment with equality. In this paper, we specialise the monodic resolution method to the guarded monodic fragment with equality and first-order temporal logic over expanding domains. We introduce novel resolution calculi that can be applied to formulae in the normal form associated with the clausal resolution method, and state correctness and completeness results.

Towards the Implementation of First-Order Temporal Resolution: the Expanding Domain Case

First-order temporal logic is a concise and powerful notation, with many potential applications in both Computer Science and Artificial Intelligence. While the full logic is highly complex, recent work on monodic first-order temporal logics has identified important enumerable and even decidable fragments. In this paper, we develop a clausal resolution method for the monodic fragment of first-order temporal logic over expanding domains. We first define a normal form for monodic formulae and then introduce novel resolution calculi that can be applied to formulae in this normal form. We state correctness and completeness results for the method. We illustrate the method on a comprehensive example. The method is based on classical first-order resolution and can, thus, be efficiently implemented.

System for Automated Deduction (SAD): Linguistic and Deductive Peculiarities

In this paper a state of the art of a system of automated deduction called SAD is described . An architecture of SAD corresponds well to a modern vision of the Evidence Algorithm programme, initiated by Academician V.Glushkov.

Stratified resolution

We introduce a calculus of stratified resolution, in which special attention is paid to clauses that "define" relations. If such clauses are discovered in the initial set of clauses, they are treated using the rule of definition unfolding, i.e. the rule that replaces defined relations by their definitions. Stratified resolution comes with a powerful notion of redundancy: a clause to which definition unfolding has been applied can be removed from the search space. To prove the completeness of stratified resolution with redundancies, we use a novel combination of Bachmair and Ganzingerâ??s model construction technique and a hierarchical construction of orderings and least fixpoints.

Searching for Invariants Using Temporal Resolution

In this paper, we show how the clausal temporal resolution technique developed for temporal logic provides an effective method for searching for invariants, and so is suitable for mechanising a wide class of temporal problems. We demonstrate that this scheme of searching for invariants can be also applied to a class of multi-predicate induction problems represented by mutually recursive definitions. Completeness of the approach, examples of the application of the scheme, and overview of the implementation are described.