Model != World?
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From: Tegiri Nenashi on 4 Jan 2010 16:44 Excuse me, but I have a basic question. What is the motivation for differentiating the concepts of "World" and "Model"?
From: Jan Hidders on 4 Jan 2010 17:33 On 4 jan, 22:44, Tegiri Nenashi <tegirinena...(a)gmail.com> wrote: > Excuse me, but I have a basic question. What is the motivation for > differentiating the concepts of "World" and "Model"? The term model is usually used for the complete structure for which we define the truth value of a formula. In conventional logic this is usually a model of the particular world we assume we are in. However, in modal logic this includes the complete set of possible worlds plus the particular world we assume we are in. Both are needed since for basic propositions we need to inspect the actual world and the modal operators refer also to the other possible worlds. -- Jan Hidders
From: Daryl McCullough on 4 Jan 2010 17:34 Tegiri Nenashi says... >Excuse me, but I have a basic question. What is the motivation for >differentiating the concepts of "World" and "Model"? You could think of each possible world as a different model of a theory. That works. (Although there may need to be certain constraints on what models of a theory are under consideration). But the philosophical discussion of what's possible, and what's necessary, and alternative possible worlds predates modern model theory. One thing that is different about modal logics is that ability to refer to multiple possible worlds (any time you say that something is possible, you are implicitly quantifying over possible worlds). It's not usual in model theory to allow quantification over models in the object language (although such quantification may take place in the metalanguage). When you consider propositions involving modal operators, a single "possible world" is not a model for such propositions. It's the entire structure of all possible worlds that is being referred to by statements such as: "It is necessarily the case that X". There is a discussion of the various uses of possible worlds here: http://www9.georgetown.edu/faculty/ap85/papers/PhilThesis.html but there is no mention of the fact that a possible world is a model of a theory. -- Daryl McCullough Ithaca, NY
From: Vadim Tropashko on 4 Jan 2010 20:56 On Jan 4, 1:44 pm, Tegiri Nenashi <tegirinena...(a)gmail.com> wrote: > Excuse me, but I have a basic question. What is the motivation for > differentiating the concepts of "World" and "Model"? Model (aka structure) is an ordered triple <domain (aka universe), signature, and interpretation function>. Now, assuming "universe = world" we have "world != model". QED.
From: vldm10 on 4 Jan 2010 21:59
On Jan 4, 10:44 pm, Tegiri Nenashi <tegirinena...(a)gmail.com> wrote: > Excuse me, but I have a basic question. What is the motivation for > differentiating the concepts of "World" and "Model"? Here you can find the precise definition for model for First-order modal logic: http://drona.csa.iisc.ernet.in/~deepakd/logic/modal_logic.ppt. and for Higher-order modal logic: http://comet.lehman.cuny.edu/fitting/bookspapers/pdf/papers/HighOrdPaper.pdf Definition for model for classical logic is: A model is every structure S = ( A, F, R, C), where A is a non-empty set, (A, F, C) is an algebra and R is set of relations over A. Vladimir Odrljin |