Lecture02WFFsAndTruthTables

Lecture02WFFsAndTruthTables - Lecture 2 - CS 2603 Applied...

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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 1 Lecture 2 —CS 2603 Applied Logic for Hardware and Software Proofs Propositions and Calculuses
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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 2 Logic a tool for careful reasoning ± Software and hardware development 9 Used in integrated circuit (computer chip) design 9 Used in safety-critical hardware/software (eg, avionics) 9 Used in secure hardware/software systems 9 Positive influence on all hardware/software development ± Hardware are software are logic 9 Hardware circuits are physical representations of formulas in logic 9 Software artifacts are, literally, formulas in logic 9 So, the goal of defect-free hw/sw is as attainable as any other goal in mathematics ± Foundation for programming languages 9 Lambda calculus – semantic base for all PLs 9 Type checking and type inference – basis in logic ± Artificial intelligence, database systems 9 Grounded in formal logic
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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 3 Propositional Logic a ll t h r e c o n s i te S ar g H ± Proposition – atomic entity, true or false 9 Capital letters denote propositional variables – Standing for specific propositions – P, Q, … specific propositions - value: true or false 9 Lowercase letters are metavariables – Denoting propositional formulas – a, b, … value: formula, such as P, (P Q), … ± Calculus 9 a method of reasoning by computation of symbols ± Infinitesimal calculus 9 Slopes and areas under continuous curves 9 This class is not about infinitesimal calculus ± Propositional Calculus 9 scheme for calculating with logic formulas ± Three different Propositional Calculuses 9 Semantics-based reasoning – truth tables 9 Syntax-based reasoning – inference rules 9 Equational reasoning – Boolean algebra
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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 4 Logical Operators Logical And P Q, (P Q)
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Lecture02WFFsAndTruthTables - Lecture 2 - CS 2603 Applied...

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