# How to Prove “Possibly P if Necessarily P” in Kripke Modal Logic?

## Does necessity imply possibility?

Possibility and necessity are related. Something is possible if its failing to occur is not necessary; if something is necessary, its failure to occur is not possible.

## What is modal logic with example?

Even in modal logic, one may wish to restrict the range of possible worlds which are relevant in determining whether ◻A is true at a given world. For example, I might say that it is necessary for me to pay my bills, even though I know full well that there is a possible world where I fail to pay them.

## What is modal proposition in logic?

Any proposition at least one of whose constituent concepts is a modal concept is a modal proposition. All other propositions are nonmodal. Any modal proposition can be represented in our conceptual notation by a wff containing one or more modal operators, e.g., “•”, “0”, etc.

## Is modal logic classical logic?

Every regular modal logic is classical, and every normal modal logic is regular and hence classical.

## How do you know if something is logically possible?

Logical possibility is usually considered the broadest sort of possibility; a proposition is said to be logically possible if there is no logical contradiction involved in its being true.

## What is the modality possibility?

Modality: Modality is the study of possibility and necessity. These concepts are intuitive enough. Possibility: Some things could have been different. For instance, I could have been a truck driver. Britain could have won the Revolutionary War.

## What does Epistemically possible mean?

An epistemic possibility is something that may be true, given the relevant epistemic constraints (for example, “Given what we know about the weather, it might rain tomorrow”), while an epistemic necessity is something that must be true given the relevant epistemic constraints (for example, “I don’t see Julie’s car in …

## How does possible worlds semantics define a necessary proposition?

Necessarily true propositions (often simply called necessary propositions) are those that are true in all possible worlds (for example: “2 + 2 = 4”; “all bachelors are unmarried”).

## What does logical necessity mean?

When something is logically necessary, it is true by definition. These can also be called analytic truths. If we can prove that something is true because “it could not be otherwise,” then it is logically necessary. The statement is true with an absolute degree of certainty.

## What is necessity and contingency?

Quick Reference. A necessary truth is one that could not have been otherwise. It would have been true under all circumstances. A contingent truth is one that is true, but could have been false.

## What is a necessary proposition?

necessary proposition was a proposition which it is necessary for us. men to believe, or for some of us to believe. A proposition could. be necessary for us to believe because it had not occurred to us to. doubt it, or because it -seemed to us obviously true, or because.