Sentence examples for logical matrix from inspiring English sources

Given a logic L, a logical matrix < A, D > is said to be a model of L if wherever Γ ⊢L φ then every valuation v on A that maps the elements of Γ to some designated value (i.e. an element of D) also maps φ to a designated value.

The outcome was the family of Gödel systems, and a result, namely, that intuitionistic logic does not have a characteristic logical matrix with only finitely many truth degrees.

For Suszko, the set of truth values assumed in a logical matrix for a many-valued logic is a set of "admissible referents" (called "algebraic values") of formulas but not a set of logical values.

The video frames were converted into a corresponding logical matrix.

In addition, the transition matrix of the pinning control is given by solving some logical matrix equations.

As we will see the perspective changes in an important respect from the perspective taken by logical matrix model theory.

The abstract logics that we are going to define can be seen, in contrast to logical matrices, as algebraic generalizations of the logic itself and its extensions.

The class of protoalgebraic logics turned out to be the class of logics for which the theory of logical matrices works really well in the sense that many results of universal algebra have counterparts for the classes of reduced matrix models of these logics; consequently the algebraic study of protoalgebraic logics using their matrix semantics has been very fruitful.

Moreover, they were also used to define sets of formulas with similar properties to the ones the sets of theorems of the known logical deduction systems have, in particular the property of being closed under substitution instances and more recently logical matrices have also been used to define logics as consequence relations.

Logical matrices where first used as models of the theorems of specific logic systems, for instance in the work of McKinsey and Tarski, and also to define sets of formulas with similar properties to the set of theorems of a logic system, namely closure under substitution instances.

These pairs are the logical matrices.