Post by Eugene 2.0 on Jun 10, 2022 18:03:49 GMT
Jan Lukasiewicz (a Polish philosopher) had the beginnings of 4-valued and multivalued logics, but it is known that the general model for multivalued logics was performed by E. Post (an American philosopher). However, all multivalued n+2 models of logic in one way or another, only aspect expand the two-valued. However, modal interpretations are always interesting for any intermediate value, in particular, it is a comparison of the neutrality of the meanings of statements with their modal coloring.
For example, you can use the following expression:
or formally:
where, the value of P = 0.5 (ie, any neutral value). And let us explain at once that modality should be understood as the presence of at least one interpretation among possible worlds, and neutral meaning (according to Lukasiewicz) as one that does not say whether this statement is false or true, but only presupposes it.
Again, according to Lukasiewicz, some expression A, meaning 0.5, should be understood as a system:
That is, the sentence is either true or false (not disjunctive and not conjunctive). As a result of this interpretation, the negation of a sentence with a neutral value gives a neutral value, and the false consequence B in the formula
also gives a definite result of 0.5 - non-classical value. Thus, we have many cases with a neutral value in the propositional formulas. In modal formulas, these meanings acquire some additional uncertainty, primarily semantic. Note:
that, at a value of 0.5 should be understood as:
But it cannot be that we have opposite meanings. And although we do not have conjunctions in the system, we also cannot semantically identify them, because these are two interpretations that contradict each other. So, there is only this:
However, it is unclear exactly how to deal with the denial of the system. However, we can only say that a neutral value will be equivalent to only a neutral one. Thus, there are some doubts about the existence of the same interpretation of the value of 0.5 in three-digit logic as in its modal equivalent. At least, these doubts are not unfounded.
Returning to the first sentence, we should turn to the possibility of interpreting Lukasiewicz's non-classical logic - because we have the modality "possible" (◊) - at the same time, the very status of such a sentence as neutral indicates that it is or is possible or not ... That is, back to the strange interpretation.
In fact, all these formal aspects could be solved by tabular methods, where the value 0.5 would have a different interpretation, for example, in four-digit logic, as 0;1;0 (Lukasiewicz or Post), but not the formal side, but the semantic some doubts. Neutral meaning is questionable in modal logic no less, compared to the usual.
In conclusion, we take into account that the complexity of logic significantly complicates their interpretation, especially in cases where the meaning of some coincides with the meanings of others. And I do not reinforce this coincidence at all, but on the contrary - it reduces the level of intelligibility of formulas.
For example, you can use the following expression:
"It is possible that the neutral statement of P is neutral"
or formally:
◊P = 0.5
where, the value of P = 0.5 (ie, any neutral value). And let us explain at once that modality should be understood as the presence of at least one interpretation among possible worlds, and neutral meaning (according to Lukasiewicz) as one that does not say whether this statement is false or true, but only presupposes it.
Again, according to Lukasiewicz, some expression A, meaning 0.5, should be understood as a system:
{x = 1
{x = 0
That is, the sentence is either true or false (not disjunctive and not conjunctive). As a result of this interpretation, the negation of a sentence with a neutral value gives a neutral value, and the false consequence B in the formula
А⊃В
also gives a definite result of 0.5 - non-classical value. Thus, we have many cases with a neutral value in the propositional formulas. In modal formulas, these meanings acquire some additional uncertainty, primarily semantic. Note:
□Р
that, at a value of 0.5 should be understood as:
{□P = 1
{□P = 0
But it cannot be that we have opposite meanings. And although we do not have conjunctions in the system, we also cannot semantically identify them, because these are two interpretations that contradict each other. So, there is only this:
□Р = 0.5. ⊃ ~◊{P = 1; P = 0}
However, it is unclear exactly how to deal with the denial of the system. However, we can only say that a neutral value will be equivalent to only a neutral one. Thus, there are some doubts about the existence of the same interpretation of the value of 0.5 in three-digit logic as in its modal equivalent. At least, these doubts are not unfounded.
Returning to the first sentence, we should turn to the possibility of interpreting Lukasiewicz's non-classical logic - because we have the modality "possible" (◊) - at the same time, the very status of such a sentence as neutral indicates that it is or is possible or not ... That is, back to the strange interpretation.
In fact, all these formal aspects could be solved by tabular methods, where the value 0.5 would have a different interpretation, for example, in four-digit logic, as 0;1;0 (Lukasiewicz or Post), but not the formal side, but the semantic some doubts. Neutral meaning is questionable in modal logic no less, compared to the usual.
In conclusion, we take into account that the complexity of logic significantly complicates their interpretation, especially in cases where the meaning of some coincides with the meanings of others. And I do not reinforce this coincidence at all, but on the contrary - it reduces the level of intelligibility of formulas.