In this paper we define a class of polyadic algebras (Q-algebras) as adequate algebraic structures for the logic with the quantifier "there exist uncountably many". The main result is a representation theorem for the countableQ-algebras of countable deg...
as it is used in acompound sentence. For instance, the sentence "It is raining or it is snowing" implies that only one of these two events is occurring. However, when the OR symbol is used as a connective function in analgebraic expression, it is possible for both...
universal-algebraic point of view, and the structure of the set of all the full generalized models of S on a fixed algebra A from the lattice-theoretical point of view; this set is represented by the lattice FACSs A of all algebraic closed-set systems C on A such that (A, C) ε.....
of real numbers to exact precision. Numbers can be added, subtracted, multiplied, and divided. Numerical calculations or numerical computations involve performing these operations. For example, if the symbol * is used to represent multiplication and / is used to represent division, then the equation...
The application hands a data-structure to an intermediate-format symbol that responds with how many pieces to divide the data into, each of those pieces can then repeat the pro-cess. Fourth, easy-to-use high level languages exist that compile down to the format, including a backwards ...
Algebraic structures of truth values in fuzzy control It is well known that in two-valued logic the set of truth values 0 and 1 with the logical operations AND(∧), OR(∀) and NOT(⌍) satisfy the axioms of Boolean algebra. The characteristics of Boolean algebra provide the fundamental ...
Abstract: The mathematical knowledge system is a complex network with multiple levels and dimensions, and its construction and development cannot be separated from multiple core components such as l…
Using algebraic data types has several advantages:Pattern matching can be used to analyze any concrete instance to select different behaviour based on input data. as in the example that maps Status to Severity there is no need to use if..then..else.. constructs. The compiler can detect ...
1.(Mathematics) a mathematical statement that two expressions are equal: it is either anidentityin which the variables can assume any value, or aconditional equationin which the variables have only certain values (roots) 2.the act of regarding as equal; equating ...
Symbols like x can be used to represent algebraic variables or “unknowns”. This is central to doing many kinds of mathematics in the Wolfram Language. LeafCount gives the total number of atoms at the leaves of an expression tree. ByteCount gives the number of bytes needed to store the ...