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In mathematical logic, a propositional variable (also called a sentence letter, [1] sentential variable, or sentential letter) is an input variable (that can either be true or false) of a truth function. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher-order logics.
For example, 3 variables produces 2 3 = 8 rows and 8 Karnaugh squares; 4 variables produces 16 truth-table rows and 16 squares and therefore 16 minterms. Each Karnaugh-map square and its corresponding truth-table evaluation represents one minterm.
PDL blends the ideas behind propositional logic and dynamic logic by adding actions while omitting data; hence the terms of PDL are actions and propositions. The TV example above is expressed in PDL whereas the next example involving := + is in first-order dynamic logic. PDL is to (first-order) dynamic logic as propositional logic is to first ...
variables denoting time moments t 1,t 2,t 3,... variables denoting time intervals n 1,n 2,n 3,... The set of terms (denoted by S) is constructed as follows: variables denoting time moments or intervals are terms; if and is a time interval variable, then (,) The set of formulas (denoted by For) is constructed as follows: [10]
In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable.It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings.
For the pair a, b there are 2 2 =4 possible interpretations: 1) both are assigned T, 2) both are assigned F, 3) a is assigned T and b is assigned F, or 4) a is assigned F and b is assigned T. Given any truth assignment for a set of propositional symbols, there is a unique extension to an interpretation for all the propositional formulas built ...
In this example propositional logic assertions are checked using functions to represent the propositions a and b. The following Z3 script checks to see if a ∧ b ¯ ≡ a ¯ ∨ b ¯ {\displaystyle {\overline {a\land b}}\equiv {\overline {a}}\lor {\overline {b}}} :
In logic, linear temporal logic or linear-time temporal logic [1] [2] (LTL) is a modal temporal logic with modalities referring to time. In LTL, one can encode formulae about the future of paths, e.g., a condition will eventually be true, a condition will be true until another fact becomes true, etc.