Abstract

Many logic handbooks allude to the obvious connection between propositional logic and logic circuits. Truth functions in logic can be represented by logic circuits in which the high or low voltage levels of the circuits correspond to the true and false logic values, respectively. At the propositional logic level, the logical connectives of propositions can be simulated by logic circuits as follows: the true or false logical evaluation of atomic propositions corresponds to the high or low level of the circuit input and the truth value of compound propositions corresponds to the circuit output state. A high circuit output signifies that the compound sentence is evaluated as true, whereas a low output indicates that the compound sentence is false. It is well known that in the world of logic circuits, the AND connective in logic corresponds to the AND gate, the OR connective to the OR gate and the negation operation to the inverter. The output of a circuit equivalent to contradiction is always low and that of a circuit corresponding to tautology is always high irrespective of the input state. The remaining compound formulas correspond to logic circuits with a high output level for some inputs and low output level for other inputs. However, what logical circuit can model a circular sentence?