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Modal operator

From Wikipedia, the free encyclopedia

A modal connective (or modal operator) is a logical connective for modal logic. It is an operator which forms propositions from propositions. In general, a modal operator has the "formal" property of being non-truth-functional in the following sense: The truth-value of composite formulae sometimes depend on factors other than the actual truth-value of their components. In the case of alethic modal logic, a modal operator can be said to be truth-functional in another sense, namely, that of being sensitive only to the distribution of truth-values across possible worlds, actual or not. Finally, a modal operator is "intuitively" characterized by expressing a modal attitude (such as necessity, possibility, belief, or knowledge) about the proposition to which the operator is applied.[1]

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  • John Grinder & NLP Meta Model, the logic of Modal Operators
  • Modal Propositional Logic - Symbols and Syntax
  • A Quick Introduction to Modal Logic, part 1

Transcription

so, in the original work published "Structure of magic Vol. 1" with the metamodel appeared for the first time visually Bandler and I called it "Modal Operators" we borrowed this term...the three levels of logic ... are typically going to confront when you take the university level in logic there's the A is true B is true what's the truth value of A and B so, that's the most basic propositional logic and then you get quantification all humans are mortal Simon's a human, Simon's a mortal and then the quantification of some of blablabla and finally the third level is model opertors and that's what we are doing here the must, can, can't must... have to, etc now that's sort of the background for where the name comes from and if you're interested it gives you a screen to pull and go back and see what they've actually done informalizing what we plan to do in terms this application is a and it's used in the metamodel it's primarily a way of identifying the edges of somebodys thinking if in fact the verbal productions that people made are reasonably a faithful reflection of the thinking patterns in our systems, visual, auditory, kinaesthetic, etc as well as verbal then you've been treated to a gift they just told you where the edge of their map is what are the challenges if I say to you: "We can't do this"? what are the challenges? and you challenge that? yes, but what specific verbal challenge we make to a statement in other words, like "we can't do that" "we can't do the programme we've just done there's actually two challenges one points to the future and one points to the past so if I say: "we can't do this" and you say: "what stops us?" you ask: "what's is the impediment? what is the obstacle?" "what is is in the world that makes it impossible or you can't do this particular thing?" so you are asking for sort of what's the obstacle? which is really a past present oriented question the other one is more interesting what would happen if we did? and that gold is business, in research, in management practice, in family it'll take a little extra time with your teenagers but they should be taught this "You can't go to the dance" "mum, but what happened if I did?" there may be an answer to that or may not but it will teach the child as they move into other parts of their life to identify intuitively this sort of conversational hinders and to push past it and explore the consequences of doing things that you're claimed you cant' do "I can't do x" or "what happen if you did" "I must do x" or "what happen if you didn't" so it's the same challenge there's a flip in the affirmative mediation parts of it, so it's that part clear? it's that challenge clear? and to me of the challenges that you can make this is the most profitable the boss says: "Yeah, great idea but we can't implement that" "boss, excuse me, respectfully help me understand, but what happen if we did?" and now you've opened a conversation you're doing a research project I can't get the results that I'm attempting to get but what would happen if you did or in that case that is quite useful to ask "what specifically stops you? what's the impediment?" so, the question which I endorse unequivocally is "what would happen if you did?" "what would happen if you didn't?" depending on whether is a can't or must and the one that explores the present obstacles doing that and the past ones is "what stops you for doing that?" what makes you do depending on whether it's a have to-must or unable-can't so, if somebody says, you know "we have to do this" and you go or "we can do this" and somebody... and you respond with "what stops you? or what stops us?" there's an implication that there's a cause-effect relationship between the thing you are proposing and the present obstacles in the world and I don't like much endorsing any cause effect in human discourse so, I'm very sympathetic to those proposal here and that's why I have been endorsing the future question of what happen if we did do it what would happen if we didn't do it must or can, etc but sometimes if you ask what prevents you you can actually take you into unresourceful... it often does, and notice, you know there's always moms going "Why can't you clean up your room before you leave in the morning?" so, often such things lead to as you correctly stated states of inaptitude essentially you would justify the thing that you can't do as opposed to explore the consequences of what would happen if you did do the thing the consequences exploration is what I endorse here not the investigation of what stops you the cause of the implications but the cause effect is implicit in the question but that is a good question what will happen if you did take time and that's like... - But I don't have time - you never have time? what if you substitute reading a book for this ridiculous conversation we are having right now so, there's always a relative device to the immediate experience move which I endorse - How to actually get her out of that she's living in second position she is living a the service of the means of other people there's no first position well developed otherwise this wouldn't be an issue the issue actually runs deeper the conversation we talk about earlier this morning about people who don't have first position how do you develop that but is not a bad beginning to go: "well, you don't have... you can't do it because you don't have time you always are busy always you never sleep, you never stop you find yourself you can explore that issue what would happen if you did take the time and reduced the commitment to these other activities spread it out over a long... you know lots of ways to negotiate it but underneath I think you are gonna uncover the lack of the well developed first position she doesn't know what she wants my mum was a complete exception she was... she was her own person but in her generation women in the States were sort of evaluated on knowing what the needs of their children and husbands were before they knew what their needs were and the other way encompasses by living in their in their position so... sense, calibrate, second position and that's why the "empty nest " syndrome was so strong in their generation once the children are gone suddenly you're confronted with this person who... your husband, your wife and you know there's nothing to be done and now suddenly you are confronted with the void what I'm gonna do with my life - that's when they go and buy the most expensive car they can find - often it resolves in some cases the so called mid-life crisis they try fill the void with things material things - How do you develop a first position? - I so don't have any idea (laughs) It's always, I've always known what I want that helps immensly and sort of presuppose the first position I can sense what I want If you ever get the chance to watch Carmen Bostic at a buffet it's very instructive she'll walk through the buffet sniffing, looking, pausing and she will take nothing and assume she's has the time and she goes back and she'll get a plate and she walk up and stand in front of this offering waiting for a movement or a lack of movement so she let's her unconscious pick the portions and the sequences and conbinations which are healthiest as far as the human body can there's a lot of other things to say about eating and weight management and so forth we are very corrupted by sugar and refined flour and so forth in the most of western European cultures but there's an old experiment happened in the... late 30's I think take an infant, year an half who can more or less feed themselves and give them what at the time in this era were consider the major food groups which in some proportionality were consider to be a perfect diet It's changed behind each our attempts to make this happen but nevertheless you can give the kid let the kid feed itself and cover the floor around then you weight the containers and you keep track of how much of each one of his major food groups over any single feeding or any single day or any single series of 4 or 5 days horribly unbalanced diet over about a week or 10 days he starts to close on average and this is sometimes you heard wisdom of the body notice I use a year and a half old baby as the model here because they are less corrupted by the things I just mentioned, sugar and refined flours so there's something very nice about having enough self calibration sensitivity to what you need in your body that you seek certain things automatically and if you have access to those sensations and you can allow the to unfold rather than overriding them with more conscious decisions about I want something sweet

Syntax for modal operators

The syntax rules for modal operators and are very similar to those for universal and existential quantifiers; In fact, any formula with modal operators and , and the usual logical connectives in propositional calculus () can be rewritten to a de dicto normal form, similar to prenex normal form. One major caveat: Whereas the universal and existential quantifiers only binds to the propositional variables or the predicate variables following the quantifiers, since the modal operators and quantifies over accessible possible worlds, they will bind to any formula in their scope. For example, is logically equivalent to , but is not logically equivalent to ; Instead, is logically equivalent to .

When there are both modal operators and quantifiers in a formula, different order of an adjacent pair of modal operator and quantifier can lead to different semantic meanings; Also, when multimodal logic is involved, different order of an adjacent pair of modal operators can also lead to different semantic meanings.

Modality interpreted

There are several ways to interpret modal operators in modal logic, including at least: alethic, deontic, axiological, epistemic, and doxastic.

Alethic

Alethic modal operators (M-operators) determine the fundamental conditions of possible worlds, especially causality, time-space parameters, and the action capacity of persons. They indicate the possibility, impossibility and necessity of actions, states of affairs, events, people, and qualities in the possible worlds.

Deontic

Deontic modal operators (P-operators) influence the construction of possible worlds as proscriptive or prescriptive norms, i.e. they indicate what is prohibited, obligatory, or permitted.

Axiological

Axiological modal operators (G-operators) transform the world's entities into values and disvalues as seen by a social group, a culture, or a historical period. Axiological modalities are highly subjective categories: what is good for one person may be considered as bad by another one.[clarification needed]

Epistemic

Epistemic modal operators (K-operators) reflect the level of knowledge, ignorance and belief in the possible world.

Doxastic

Doxastic modal operators express belief in statements.

Boulomaic

Boulomaic modal operators express desire.

References

  1. ^ Garson, James (2021). "Modal Logic". The Stanford Encyclopedia of Philosophy (Summer 2021 ed.). Metaphysics Research Lab, Stanford University. Retrieved 5 February 2024.
This page was last edited on 5 February 2024, at 23:31
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