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Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…
Outlier hypothesis testing is studied in a universal setting. Multiple sequences of observations are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are distributed…
Semantic theories of natural language associate meanings with utterances by providing meanings for lexical items and rules for determining the meaning of larger units given the meanings of their parts. Meanings are often assumed to combine…
We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be…
Universal outlier hypothesis testing is studied in a sequential setting. Multiple observation sequences are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…
Understanding the 3D world from 2D images involves more than detection and segmentation of the objects within the scene. It also includes the interpretation of the structure and arrangement of the scene elements. Such understanding is often…
The intuitive notion of evidence has both semantic and syntactic features. In this paper, we develop an {\em evidence logic} for epistemic agents faced with possibly contradictory evidence from different sources. The logic is based on a…
For more than fifty years, taxonomists have proposed numerous alternative definitions of species while they searched for a unique, comprehensive, and persuasive definition. This monograph shows that these efforts have been unnecessary, and…
We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of concept combination of prototypical concepts. The proposed logic relies on the logic of typicality ALC TR, whose semantics is based on the…
The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown…
From an inconsistent database non-trivial arguments may be constructed both for a proposition, and for the contrary of that proposition. Therefore, inconsistency in a logical database causes uncertainty about which conclusions to accept.…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…
Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only…
Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of…