Practical Non-monotonic Reasoning

1994

ion is a weil known mechanism in reasoning about individuals in concept-based systems. It consists in retrieving all the assertions relevant to a given individual a and collecting them into a single concept. Such concept has the property of being the most specific concept (expressible in the language) such that the individual a is an instance of. For this reason it is generally indicated by MSC(a) (Most Specific Concept). Abstraction, together with subsumption, allows one to perform instance checking. In fact, an algorithm for checking whether A 1= C(a) can work as follows: Step 1. compute MSC(a). Step 2. check whether C subsurnes MSC(a). This algorithm, called Abstraction/Subsumption, has been broadly exploited in actual systems (see [Quantz and Kindermann,1990; Nebel,1990]) . However, the problem of exploiting this algorithm is that, in general, it is not possible to completely fit in the information relevant to an individual into a single concept of the language. Let us clarify t...

SpringerBriefs in Computer Science, 2012

Mathematical Logic Quarterly, 1975

2007

There are two major formalisms that are developed around concepts. The first one is Formal Concept Analysis (FCA) by R. Wille and B. Ganter. Roughly speaking, FCA is an extension of algebraic Lattice Theory for knowledge representation. The second formalism, Description Logic (DL), goes back to the universal terminological logic by P.F. Patel-Schneider. It is closely related to modal and program logics. DL is widely used for ontology research, design, and implementation. Since both formalism use concepts and are used for closely related purposes, it is very natural to compare and combine them. In this paper we introduce and study variants of DL extended by three constructs motivated by FCA. Intentional semantics of two of the new constructs are new modalities that correspond to 'intent' and 'extent' (two major algebraic constructions of FCA). The third new construct is a connective that is designed to express the 'formal concept' property. If L is a variant of DL then we call L extended by these new constructs by L for FCA and denote this logic by L/FCA. We compare expressive powers of L/FCA and L(¬, −) -another variant of L extended by role complement ¬ and inverse − simultaneously. We demonstrate that L/FCA can be expressed in L(¬, −). It implies that for the basic description logic ALC, ALC/FCA is decidable.

Principles of knowledge …, 1996

Description Logics stem from Semantic Networks and Frames. They deal with the representation of structured concepts, and reasoning with them. The structure of a concept is described using a language, called concept language, comprising boolean operators (conjunction, disjunction, negation) and various forms of quanti cation over the attributes (or, roles) of the given concept. A noticeable di erence with other structuring formalisms is that also roles can be given some internal structure, e.g. a role can be expressed as a conjunction of two other roles.

2012

To my wife, Gill, without whose encouragement and support it could not have been completed Contents Acknowledgements vi In working on the matters discussed in this book, I have received help, advice, criticism and encouragement from many students, friends and colleagues. I would particularly like to thank my colleagues in the Department of Logic and Metaphysics at St Andrews for allowing me to take study leave in 1987, during which time this book was completed. I was also fortunate to be invited to the Australian National University to a three-month Visiting Fellowship during this time. I am especially grateful to Michael MacRobbie for arranging for the invitation, and for providing me with such a stimulating research environment. I am indebted to the Australian National University, the British Academy, the British Council and the University of St Andrews for financial assistance which made the visit possible.

AHTI-VEIKKO PIETARINEN, A graphical method for non-classical logics. The design of graphical languages for different logics dates back to the late 19th century but was subsequently forgotten. By graphical languages we mean those that use nonlinear, nontabular, and occurrence-referential notations. We can redesign such languages for a range of nonclassical logics that preserve the deep-inferential nature of their transformation rules. This talk presents such cases for graphical intuitionistic, bi-intuitionistic, and Brouwer logics. The 16th Asian Logic Conference was held on June 17-21, 2019, at the Nazarbayev University, Nur-Sultan, Kazakhstan. It was the second Asian Logic Conference since its status changed from an ASL-sponsored meeting to an official ASL meeting by ASL Council action in May 2016. The Asian Logic Conference (ALC) is a major international event in mathematical logic. It features the latest scientific developments in the fields in mathematical logic and its applications, logic in computer science, and philosophical logic. The ALC series also aims to promote mathematical logic in the Asia-Pacific region and to bring logicians together both from within Asia and elsewhere to exchange information and ideas.

Handbook of Automated …, 2001

2000

In order to ensure a reasonable and predictable behaviour of a Description Logic (DL) system, reasoning in the DL employed by the system should at least be decidable, and preferably of low complexity. Consequently, the expressive power of the DL in question must be restricted in an appropriate way. If the imposed restrictions are too severe, however, then the important notions of the application domain can no longer be expressed. Investigating this trade-o between the expressivity of DLs and the complexity of their inference problems has thus been one of the most important issues in DL research.

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