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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.
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.
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 ...
The predicate calculus goes a step further than the propositional calculus to an "analysis of the inner structure of propositions" [4] It breaks a simple sentence down into two parts (i) its subject (the object (singular or plural) of discourse) and (ii) a predicate (a verb or possibly verb-clause that asserts a quality or attribute of the object(s)).
Z3 was open sourced in the beginning of 2015. [3] The source code is licensed under MIT License and hosted on GitHub. [4] The solver can be built using Visual Studio, a makefile or using CMake and runs on Windows, FreeBSD, Linux, and macOS. The default input format for Z3 is SMTLIB2.
In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (x) that is not defined or specified (thus being a free variable), which leaves the statement undetermined.
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.
Some authors also admit propositional variables in first-order logic, which must then also be interpreted. A propositional variable can stand on its own as an atomic formula. The interpretation of a propositional variable is one of the two truth values true and false. [3]