Abstract

Every truth function corresponds to an isomorphic digital circuit. Consequently, the logical structure of every proposition can be presented within the range of propositional logic as an equivalent digital circuit. Provided that the logical values "true" and "false" correspond to the "high" and "low" voltage levels, the output of a circuit being equivalent with contradiction is always low level for every input state, whereas the output of a circuit corresponding to a tautology is always high level, irrespective of the input states. On the other hand, the remaining propositions correspond to circuits whose output is high-level if and only if certain atomic components of the proposition are true, and the rest of the atomic components are false. The inputs equivalent to the atomic propositions are either high or low level. However, what logical circuits are equivalent to a circulating statement or argumentation? The propositions are true or false irrespective of time, whereas the voltage level of the circuits can change over time. To be more precise, we can say that the input levels of the circuits are high or low depending on whether we evaluate the atomic formulae of the formula expressing the logical structure of the proposition as true or false. The voltage level of the output of the circuit corresponds to the truth value of the formula. I will call `{combinational automaton}' the digital circuit that may model the formulae of propositional logic. Formulae connected with truth functions yield formulae again. Although there are always corresponding automata for them, the situation is not simple in this case. We do not always get combined automata joined to each other, and in some cases, it is also possible that we do not get an automaton--an operating machine or circuit--at all. There are digital circuits whose output is not a function of their input. The range of automata is wider than that of combinational automata. It includes machines whose input states do not unambiguously determine the output states; that is, the output is not a function of the input. This is because the circuit has feedback. Most digital circuits belong to this latter group. I will call them "sequential automata". The question arises whether there is a logical structure of a circulating statement that corresponds to such a sequential automaton (or sequential circuit). In my view, the logical structure of the Liar Paradox coincides with the operation of a sequential automaton irrespective of the logical correctness of the paradox itself. The analysis also examines possibilities for further developing the model.