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sav08:propositional_logic_informally [2010/02/22 01:09] vkuncak |
sav08:propositional_logic_informally [2012/02/21 15:09] vkuncak |
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| ====== Propositional Logic ====== | ====== Propositional Logic ====== | ||
| - | Propositional logic is the core part of most logical formalisms (such as first-order and higher-order logic). It also describes well digital circuits that are the basis of most modern computing devices. In this course we will | + | Propositional logic is the core part of most logical formalisms (such as first-order and higher-order logic). It also describes well digital circuits that are the basis of most modern computing devices. |
| - | * review propositional logic informally to make sure everyone is comfortable with it (today) | + | |
| - | * define propositional logic formula syntax and semantics formally | + | ===== Importance of Propositional Logic ===== |
| - | * learn how to write programs that build, transform, and prove validity of such formulas (SAT solvers) | + | |
| - | * use these techniques to build verification tools | + | * Many search problems can be encoded using propositional formulas |
| + | * Checking equivalence of logical combinatorial circuits in hardware directly reduces to SAT | ||
| + | * Can encode integer arithmetic with fixed bitwidth (e.g. operations on 16-bit integers) | ||
| + | * An important class of logics can be obtained by giving meaning to propositional variables | ||
| ===== Propositional Formulas ===== | ===== Propositional Formulas ===== | ||
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| Suggest another tautology. | Suggest another tautology. | ||
| - | |||
| - | ===== Importance of Propositional Logic ===== | ||
| - | |||
| - | * Many search problems can be encoded using propositional formulas | ||
| - | * Checking equivalence of logical combinatorial circuits in hardware directly reduces to SAT | ||
| - | * Can encode integer arithmetic with fixed bitwidth (e.g. operations on 16-bit integers) | ||
| - | * An important class of logics can be obtained by giving meaning to propositional variables | ||
| ===== More information ===== | ===== More information ===== | ||