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Predicate Calculus
Published in Janet Woodcock, Software Engineering Mathematics, 1988
There are two new symbols which need to be explored further: V and 3. These are used to capture the idea of universal and existential quantification respectively. Universal quantification allows us to write propositions of the form "every object has this property" or "all objects are related in this way". They are propositions because they have an underlying truth value and conform to the rules of excluded middle and contradiction, but they are expressed in terms of predicates. A sentence of the form Vz P{x) is interpreted as the proposition "we can instantiate x by the name of any object and the resulting proposition will be true". This assertion may itself be true or false, of course.
U
Published in Phillip A. Laplante, Dictionary of Computer Science, Engineering, and Technology, 2017
universal quantification a first order logic operator used to quantify a variable over a finite or infinite set. It is used to state that a formula is true for every value of a variable. It is usually represented with V. See existential quantification.
Temporal Context-Based Delegation
Published in Applied Artificial Intelligence, 2019
Ouarda Bettaz, Narhimene Boustia, Aicha Mokhtari
For the purpose of our work, we will use TDLδε(Bettaz, Boustia, and Mokhtari 2013a), to define our delegation model. TDLδε is a temporal nonmonotonic description logic. We developed this DL to permit a better management of the time aspect in a variety of domains such as reasoning about actions and plans, enhancing natural languages comprehension and also allowing the improvement of access control. TDLδε allows representing temporal concepts while having default knowledge. Differing from the existing temporal description logics where temporal components are added to classical description logics. We present in this section the interpretation of the connectors and constants from TDLδε, and show how our approach augments the expressivity of the model while maintaining the same complexity; it actually permits to represent an exception and an exception of an exception for the context, which is not possible in OrBAC, and the use of temporal aspects allows a better representation of the delegation parameters. We then present in the upcoming sections TDL–OrBACδεand its delegation model. We will just describe the part of the syntax in Table 1 (Bettaz, Boustia, and Mokhtari 2013a) of TDLδε that we will be needing for our work, it consists of: a set of atomic concepts P and atomic roles R, the two constants ⊤ (Top) and ⊥ (Bottom) that represents, respectively, the universal and the bottom concept, a set of individuals I called ‘classic individuals’, the concepts C and D, the unary connectives δ (Default) and ε (Exception), the binary conjunction ⊓, the quantifier ∀ that enables universal quantification on role values, and the temporal qualifier @ to represent the interval ‘X’ at which a concept C applies, u is a real number, n is an integer, Ii Are ‘classic individuals’.