By A. Kurucz,F. Wolter,M. Zakharyaschev,Dov M. Gabbay
Modal logics, initially conceived in philosophy, have lately came upon many functions in computing device technology, synthetic intelligence, the rules of arithmetic, linguistics and different disciplines. Celebrated for his or her stable computational behaviour, modal logics are used as powerful formalisms for conversing approximately time, house, wisdom, ideals, activities, responsibilities, provability, and so on. even if, the great computational homes can tremendously swap if we mix a few of these formalisms right into a many-dimensional procedure, say, to cause approximately wisdom bases constructing in time or relocating objects.
To learn the computational behaviour of many-dimensional modal logics is the most target of this publication. at the one hand, it's involved in delivering a superb mathematical starting place for this self-discipline, whereas nonetheless, it indicates that many doubtless various utilized many-dimensional platforms (e.g., multi-agent platforms, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) slot in completely with this theoretical framework, and so their computational behaviour will be analyzed utilizing the constructed machinery.
We begin with concrete examples of utilized one- and many-dimensional modal logics similar to temporal, epistemic, dynamic, description, spatial logics, and diverse mixtures of those. Then we improve a mathematical thought for dealing with a spectrum of 'abstract' combos of modal logics - fusions and items of modal logics, fragments of first-order modal and temporal logics - concentrating on 3 significant difficulties: decidability, axiomatizability, and computational complexity. in addition to the normal tools of modal good judgment, the technical toolkit comprises the strategy of quasimodels, mosaics, tilings, rate reductions to monadic second-order common sense, algebraic common sense ideas. ultimately, we observe the constructed equipment and acquired effects to 3 case experiences from the sphere of data illustration and reasoning: temporal epistemic logics for reasoning approximately multi-agent structures, modalized description logics for dynamic ontologies, and spatio-temporal logics.
The style of the publication might be outlined as a study monograph. It brings the reader to front line of present study within the box by way of displaying either fresh achievements and instructions of destiny investigations (in specific, a number of open problems). nevertheless, famous effects from modal and first-order common sense are formulated with out proofs and provided with references to available sources.
The meant viewers of this booklet is logicians in addition to these researchers who use common sense in desktop technology and synthetic intelligence. extra particular software components are, e.g., wisdom illustration and reasoning, specifically, terminological, temporal and spatial reasoning, or reasoning approximately brokers. And we additionally think that researchers from yes different disciplines, say, temporal and spatial databases or geographical details platforms, will reap the benefits of this e-book as well.
• built-in method of sleek modal and temporal logics and their purposes in synthetic intelligence and computing device science
• Written through the world over prime researchers within the box of natural and utilized logic
• Combines mathematical concept of modal good judgment and functions in man made intelligence and machine science
• quite a few open difficulties for additional research
• good illustrated with photos and tables