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Vector logic [1] [2] is an algebraic model of elementary logic based on matrix algebra. Vector logic assumes that the truth values map on vectors , and that the monadic and dyadic operations are executed by matrix operators.
A vector clock of a system of N processes is an array/vector of N logical clocks, one clock per process; a local "largest possible values" copy of the global clock-array is kept in each process. Denote V C i {\displaystyle VC_{i}} as the vector clock maintained by process i {\displaystyle i} , the clock updates proceed as follows: [ 1 ]
The four valued logic of two bits, transformed by 2x2 logical matrices, ... If m or n equals one, then the m × n logical matrix (m ij) is a logical vector or bit string.
Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2 w . In mathematics and physics , a vector space (also called a linear space ) is a set whose elements, often called vectors , can be added together and multiplied ...
In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs. Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed.
Modern philosophers reject quantum logic as a basis for reasoning, because it lacks a material conditional; a common alternative is the system of linear logic, of which quantum logic is a fragment. Mathematically, quantum logic is formulated by weakening the distributive law for a Boolean algebra, resulting in an orthocomplemented lattice .
Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation.' [1] Just as group theory deals with groups, and linear algebra with vector spaces, Boolean algebras are models of the ...
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.