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Where logic meets emotion

As she sat in a taxi headed to Cairo International Airport in September 2001, Rana el Kaliouby remembers thinking, "Am I really going through with this?" A married woman and hijab-wearing Muslim, she would be on her own for the next 3 years, pursuing her doctorate in computer science at the University of Cambridge in the United Kingdom. In Girl Decoded, el Kaliouby and coauthor Carol Colman have created a riveting memoir of a "nice Egyptian girl" who, despite cultural conditioning that encouraged her to put her duties as a wife and mother first, went on to pursue her professional dreams.

From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931

Harvard University Press

Description Logics Courses and Tutorials

Enrico Franconi's Course on Description Logics The material includes slides for 6 modules ( 320 slides): A review of Computational Logics, Structural Description Logics, Propositional Description Logics, Description Logics and Knowledge Bases, Description Logics and Logics, Description Logics and Databases. A web pointer to an online modified version of CRACK, allowing for tracing satisfiability proofs with tableaux, is provided. Pointers to relevant online literature are provided, too. Enrico Franconi's Course on Description Logics The material includes slides for 6 modules ( 320 slides): A review of Computational Logics, Structural Description Logics, Propositional Description Logics, Description Logics and Knowledge Bases, Description Logics and Logics, Description Logics and Databases. A web pointer to an online modified version of CRACK, allowing for tracing satisfiability proofs with tableaux, is provided.

Neutrality and Many-Valued Logics

In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz's, Goedel's, Product, and Post's logics). The informal sense of Archimedes' axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes' axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. On the base of non-Archimedean valued logics, we construct non-Archimedean valued interval neutrosophic logic INL by which we can describe neutrality phenomena.

Characterising equilibrium logic and nested logic programs: Reductions and complexity

Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations are permitted in heads and bodies of rules, as special kinds of theories. In this paper, we present polynomial reductions of the main reasoning tasks associated with equilibrium logic and nested logic programs into quantified propositional logic, an extension of classical propositional logic where quantifications over atomic formulas are permitted. We provide reductions not only for decision problems, but also for the central semantical concepts of equilibrium logic and nested logic programs. In particular, our encodings map a given decision problem into some formula such that the latter is valid precisely in case the former holds. The basic tasks we deal with here are the consistency problem, brave reasoning, and skeptical reasoning. Additionally, we also provide encodings for testing equivalence of theories or programs under different notions of equivalence, viz. ordinary, strong, and uniform equivalence. For all considered reasoning tasks, we analyse their computational complexity and give strict complexity bounds.