Does S4 (and B) hold for the strongest interpretations of ♢ and □?

What is modal logic in philosophy?

A modal is an expression (like ‘necessarily’ or ‘possibly’) that is used to qualify the truth of a judgement. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions ‘it is necessary that’ and ‘it is possible that’.

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.

Is modal logic true?

In the most common interpretation of modal logic, one considers “logically possible worlds”. If a statement is true in all possible worlds, then it is a necessary truth. If a statement happens to be true in our world, but is not true in all possible worlds, then it is a contingent truth.

What is modal logic in computer science?

Abstract. Modal logic is a widely applicable method of reasoning for many areas of computer science. These areas include artificial intelligence, database theory, distributed systems, program verification, and cryptography theory.

What is S4 modal logic?

The flavor of (classical) modal logic called S4 is (classical) propositional logic equipped with a single modality usually written “□” subject to the rules that for all propositions p,q:Prop we have.

What are the types of modal logic?

Modal logic can be viewed broadly as the logic of different sorts of modalities, or modes of truth: alethic (“necessarily”), epistemic (“it is known that”), deontic (“it ought to be the case that”), or temporal (“it is always the case that”) among others.

What is the modal ontological argument?

To combine these concepts, modal ontological arguments are ontological arguments that invoke possibility or necessity. These arguments define God in a way that entails that he exists necessarily if he exists at all, and the conclusion is that he does in fact exist necessarily.

Who is the father of logic?

Aristotle

As the father of western logic, Aristotle was the first to develop a formal system for reasoning.

How do you read modal logic?


The box means what just means it is necessary that or necessarily the diamond means it is possible that or just possibly.

Will deontic modality?

Whether or not the verb is epistemic or deontic indicates if ‘something’ will happen or not. For example, the modal auxillary verb ‘will’ is deontic because it means that the subject of the sentence definitely will happen, whilst the modal auxillary verb ‘may’ is epistemic because the outcome is less definite.

What are modals quantifiers?

The traditional view in grammar and logic inherited from Aristotle has been that quantifiers and modals are different kinds of words. Although both are syncategorematic expressions (i.e. they don’t signify anything on their own), quantifiers modify the subject while modals modify the copula.

What is a modal proposition?

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 second order logic complete?

Several deductive systems can be used for second-order logic, although none can be complete for the standard semantics (see below). Each of these systems is sound, which means any sentence they can be used to prove is logically valid in the appropriate semantics.

What Is syntax of modal logic?

The symbols of modal logic consistute of an infinite countable set P of proposi- tional variables, logical connectives, parenthesization, and the modal operator D. The choice of logical connectives depends on the development of proposi- tional logic one wants to follow; below I choose negation and implication.

What is the modal possible?

Modal verbs express if something is certain, probable or possible. If something is possible in the future, we use ‘could’, ‘might’ or ‘may’ before the main verb to talk about it. If something is possible now or was possible in the past we add the word ‘have’ after the modal verb. This still expresses possibility.

Which modal is used for strong possibility?

Must, may, might, can’t and couldn’t are used with a present perfect verb form to show how certain a speaker is that a past situation happened or didn’t happen.

What is the modal of strong obligation?

In present, need to, must and have to are all used to express strong obligation.

Which modal below should be used if you want to depict a strong sense of obligation?

We use “must” to talk about obligations.

What is the modal of weak obligation and example?

The modal verb should expresses weaker obligation than must and have to. should be, should go, should do, etc.