https://www.cs.ox.ac.uk/people/bernardo.cuencagrau/publications/PelletDemo.pdf

Pellet: A practical OWL-DL reasoner

What is modal logic

This introduction presents the main motivations for the development of Description Logics (DLs) as a formalism for representing knowledge, as well as some important basic notions underlying all systems that have been created in the DL tradition. In addition, we provide the reader with an overview of the entire book and some guidelines for reading it. We first address the relationship between Description Logics and earlier semantic network and frame systems, which represent the original heritage of the field. We delve into some of the key problems encountered with the older efforts. Subsequently, we introduce the basic features of DL languages and related reasoning techniques. DL languages are then viewed as the core of knowledge representation systems, considering both the structure of a DL knowledge base and its associated reasoning services. The development of some implemented knowledge representation systems based on Description Logics and the first applications built with such systems are then reviewed. Finally, we address the relationship of Description Logics to other fields of Computer Science.We also discuss some extensions of the basic representation language machinery; these include features proposed for incorporation in the formalism that originally arose in implemented systems, and features proposed to cope with the needs of certain application domains.

https://assets.cambridge.org/97805218/76254/frontmatter/9780521876254_frontmatter.pdf

The Description Logic Handbook

Answer Set Programming (ASP) is a declarative problem solving approach, initially tailored to modeling problems in the area of Knowledge Representation and Reasoning (KRR). More recently, its attractive combination of a rich yet simple modeling language with high-performance solving capacities has sparked interest in many other areas even beyond KRR. This book presents a practical introduction to ASP, aiming at using ASP languages and systems for solving application problems. Starting from the essential formal foundations, it introduces ASP's solving technology, modeling language and methodology, while illustrating the overall solving process by practical examples. Table of Contents: List of Figures / List of Tables / Motivation / Introduction / Basic modeling / Grounding / Characterizations / Solving / Systems / Advanced modeling / Conclusions

/pdf/answer-set-solving-in-practice-vtcfq8bjfw.pdf

Answer Set Solving in Practice

Publisher Summary Early attempts at qualitative spatial reasoning within the qualitative reasoning (QR) community led to the poverty conjecture. The need for spatial representations and spatial reasoning is ubiquitous in artificial intelligence (AI) from robot planning and navigation to interpreting visual inputs to understanding natural language. In all these cases, the need to represent and reason about spatial aspects of the world is of key importance. Related fields of research such as geographic information science (GIScience) have also driven the spatial representation and reasoning community to produce efficient, expressive, and useful calculi. There has been considerable research in spatial representations that are based on metric measurements, in particular within the vision and robotics communities, and also on raster and vector representations in GIScience. This chapter focuses on symbolic and, in particular, qualitative representations. The challenge of qualitative spatial reasoning (QSR) is to provide calculi that allow a machine to represent and reason with spatial entities without resort to the traditional quantitative techniques prevalent in, for example, computer graphics or computer vision communities.

/pdf/qualitative-spatial-representation-and-reasoning-207okl41r9.pdf

Qualitative spatial representation and reasoning

I Introduction 1 Modal logic basics 1.1 Modal axiomatic systems 1.2 Possible world semantics 1.3 Classical first-order logic and the standard translation 1.4 Multimodal logics 1.5 Algebraic semantics 1.6 Decision, complexity and axiomatizability problems 2 Applied modal logic 2.1 Temporal logic 2.2 Interval temporal logic 2.3 Epistemic logic 2.4 Dynamic logic 2.5 Description logic 2.6 Spatial logic 2.7 Intuitionistic logic 2.8 'Model level' reductions between logics 3 Many-dimensional modal logics 3.1 Fusions 3.2 Spatio-temporal logics 3.3 Products 3.4 Temporal epistemic logics 3.5 Classical first-order logic as a propositional multimodal logic 3.6 First-order modal logics 3.7 First-order temporal logics 3.8 Description logics with modal operators 3.9 HS as a two-dimensional logic 3.10 Modal transition logics 3.11 Intuitionistic modal logics II Fusions and products 4 Fusions of modal logics 4.1 Preserving Kripke completeness and the finite model property 4.2 Algebraic preliminaries 4.3 Preserving decidability of global consequence 4.4 Preserving decidability 4.5 Preserving interpolation 4.6 On the computational complexity of fusions 5 Products of modal logics: introduction 5.1 Axiomatizing products 5.2 Proving decidability with quasimodels 5.3 The finite model property 5.4 Proving undecidability 5.5 Proving complexity with tilings 6 Decidable products 6.1 Warming up: Kn x Km 6.2 CPDL x K_m 6.3 Products of epistemic logics with Km 6.4 Products of temporal logics with Km 6.5 Products with S5 6.6 Products with multimodal S5 7 Undecidable products 7.1 Products of linear orders with infinite ascending chains 7.2 Products of linear orders with infinite descending chains 7.3 Products of Dedekind complete linear orders 7.4 Products of finite linear orders 7.5 More undecidable products 8 Higher-dimensional products 8.1 S5 x S5 x ... x S5 8.2 Products between K4 x K4 x ... x K4 and S5 x S5 x ... x S5 8.3 Products with the fmp 8.4 Between K x K x ... x K and S5 x S5 x ... x S5 8.5 Finitely axiomatizable and decidable products 9 Variations on products 9.1 Relativized products 9.2 Valuation restrictions 10 Intuitionistic modal logics 10.1 Intuitionistic modal logics with Box 10.2 Intuitionistic modal logics with Box and Diamond 10.3 The finite model property III First-order modal logics 11 Fragments of first-order temporal logics 11.1 Undecidable fragments 11.2 Monodic formulas, decidable fragments 11.3 Embedding into monadic second-order theories 11.4 Complexity of decidable fragments of QLogSU(N) 11.5 Satisfiability in models over (N,<) with finite domains 11.6 Satisfiability in models over (R,<) with finite domains 11.7 Axiomatizing monodic fragments 11.8 Monodicity and equality 12 Fragments of first-order dynamic and epistemic logics 12.1 Decision problems 12.2 Axiomatizing monodic fragments IV Applications to knowledge representation 13 Temporal epistemic logics 13.1 Synchronous systems 13.2 Agents who know the time and neither forget nor learn 14 Modal description logics 14.1 Concept satisfiability 14.2 General formula satisfiability 14.3 Restricted formula satisfiability 14.4 Satisfiability in models with finite domains 15 Tableaux for modal description logics 15.1 Tableaux for ALC 15.2 Tableaux for K(ALC) with constant domains 15.3 Adding expressive power to K(ALC) 16 Spatio-temporal logics 16.1 Modal formalisms for spatio-temporal reasoning 16.2 Embedding spatio-temporal logics in first-order temporal logic 16.3 Complexity of spatio-temporal logics 16.4 Models based on Euclidean spaces Epilogue. Bibliography. List of tables. List of languages and logics. Symbol index. Subject index.

Many-Dimensional Modal Logics: Theory and Applications

Publisher Summary This chapter surveys two key combination methods––namely, fusions and products. It also examines some other combination methods. The properties of combined logics depend on those of their components plus the particular method of combination. The idea of combining modal logics is natural for many applications. The chapter explores the way in which modal logics can be combined and highlights the consequences of combining them. The formation of fusions is the simplest and the most natural way of combining modal logics. The formation of Cartesian products of various structures—vector and topological spaces, algebras—is a standard mathematical way of capturing the multidimensional character of the world. In modal logic, products of Kripke frames are natural constructions allowing it to reflect interactions between modal operators representing time, space, knowledge, or actions. The product construction as a combination method on modal logics is introduced and is used in applications in computer science and artificial intelligence.

Combining modal logics

Spatial logic + temporal logic = ?

In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PT L, the spatial logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and 'computational realisability' within the hierarchy. We demonstrate how different combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out of components that are at most NP- or PSPACE-complete.

/pdf/combining-spatial-and-temporal-logics-expressiveness-vs-1vhlbjneqz.pdf

Combining spatial and temporal logics: expressiveness vs. complexity

https://www.dcs.bbk.ac.uk/~michael/expand.pdf

Agi Kurucz

Papers

Many-Dimensional Modal Logics: Theory and Applications

Combining modal logics

Spatial logic + temporal logic = ?

Combining spatial and temporal logics: expressiveness vs. complexity

Non-primitive recursive decidability of products of modal logics with expanding domains