Modal Logics of Topological Relations

Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the Egenhofer-Franzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns out that our modal logics have the same expressive power as the two-variable fragment of first-order logic, but are exponentially less succinct. The complexity ranges from (undecidable and) recursively enumerable to highly undecidable, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces. As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham. We also analyze modal logics based on the five RCC5 relations, with similar results regarding the expressive power, but weaker results regarding the complexity

A modal theorem-preserving translation of a class of three-valued logics of incomplete information

International audienceThere are several three-valued logical systems that form a scattered landscape, even if all reasonable connectives in three-valued logics can be derived from a few of them. Most papers on this subject neglect the issue of the relevance of such logics in relation with the intended meaning of the third truth-value. Here, we focus on the case where the third truth-value means unknown, as suggested by Kleene. Under such an understanding, we show that any truth-qualified formula in a large range of three-valued logics can be translated into KD as a modal formula of depth 1, with modalities in front of literals only, while preserving all tautologies and inference rules of the original three-valued logic. This simple information logic is a two-tiered classical propositional logic with simple semantics in terms of epistemic states understood as subsets of classical interpretations. We study in particular the translations of Kleene, Gödel, ᴌukasiewicz and Nelson logics. We show that Priest’s logic of paradox, closely connected to Kleene’s, can also be translated into our modal setting, simply by exchanging the modalities possible and necessary. Our work enables the precise expressive power of three-valued logics to be laid bare for the purpose of uncertainty management

Evolution of a Holocene, mixed-process, forced regressive shoreline: the Mitchell River delta, Queensland, Australia

Subtle changes in local accommodation, sediment flux, and wave, tide and fluvial processes can result in significant changes in the depositional style and architecture of coastal depositional systems. The detailed study of modern mixed-process depositional systems provides an opportunity to examine how such forcing factors affect shoreline evolution. The Mitchell River delta is a morphologically complex system that has prograded during a Holocene forced regression in a low accommodation epicontinental seaway. Relatively minor anthropogenic modification of the delta has occurred during the last 200 yr such that the considerable temporal and spatial variability of a mixed-influence coastal system can be observed in a de facto natural state. Of special interest is the link between preserved delta morphology and process change. A recent coastal process classification system was applied to the delta using desktop mapping and field ground-truthing and sedimentological analyses. The distribution and extent of 3400 wave-, tide- and fluvial-derived depositional elements were mapped across over 500 km2. These elements were grouped into 7 distinct progradational Element Complex Sets (ECS), defined by major reorganisations of the shoreline. The process classification of the overall delta system is tide dominated, fluvial influenced, wave affected (Tfw); however, the delta has evolved through three geometrically discrete pulses of delta progradation. The delta has evolved from (i) a symmetrical, wave-dominated, fluvial-influenced, tide-affected (Wft) system (early Holocene), to (ii) a rapidly prograding asymmetrical, tide-dominated, fluvial-influenced, wave-affected (Tfw) system (mid-Holocene), to (iii) an asymmetrical, tide-dominated, wave-influenced, fluvial-affected (Twf) system (at the modern shoreline). When the delta commenced progradation (6 ka BP), high accommodation-to-sediment-supply ratio (A/S) resulted in the deposition of wave formed depositional elements. As sea level fell and effective precipitation (EP) increased, reduced A/S resulted in more rapid progradation of tidal deposits until approximately 2 ka BP. The subsequent decrease in EP (and increased A/S) resulted in reduced rates of delta progradation and prompted multiple channel avulsions. Limited evidence suggests increased progradation rates at the modern channel mouth since 0.2 ka BP, which may be linked to increased sediment supply from anthropogenic catchment disturbance

Tidal signatures in an intracratonic playa lake

Studies of modern sediments from tide-dominated marine coastal environments in the 1970s and 1980s led to the recognition of what were suggested to be unique sedimentary features formed by tidal currents. These features could be directly related to astronomical forcing by the Sun and Moon. Sedimentary structures formed by marine tidal processes are now frequently described in modern and ancient deposits. Here, we detail similar sedimentary features from shoreline deposits of Lake Eyre, Australia, a present-day, intracratonic playa lake setting, thus challenging the current paradigm that these structures are indicative of marine tidal influence. We attribute the formation of these features in Lake Eyre to meteorological tides generated by daily changes in wind direction and velocity, along with weekly to monthly discharge variations in the feeder river system. This is the first time such sedimentary features have been documented together in a continental setting. A key implication of this is that the classic "tidal" sedimentary structures recognized in ancient rock successions should not automatically be attributed to astronomical or marine tidal currents, since similar structures can be generated by meteorological processes in continental environments. Some interpretations of ancient marine tidal deposits without other lines of evidence supporting a marine depositional environment may therefore require reevaluation. Playa lakes and shallow perennial lacustrine settings should also be considered in the interpretation of strata containing what have formerly been considered classic marine tidal indicators. © 2012 Geological Society of America.R. Bruce Ainsworth, Stephen T. Hasiotis, Kathryn J. Amos, Carmen B. E. Krapf, Tobias H. D. Payenberg, Marianne L. Sandstrom, Boyan K. Vakarelov and Simon C. Lan

OSL results: Evolution and architectural styles of a forced-regressive Holocene delta and megafan, Mitchell River, Gulf of Carpentaria, Australia

Mitchell River region optically stimulated luminescence (OSL) dating methodology and result