Diamonds and Defaults: Studies in Pure and Applied by Johan van Benthem (auth.), Maarten de Rijke (eds.)

By Johan van Benthem (auth.), Maarten de Rijke (eds.)

This quantity features a choice of papers offered at a Seminar on Intensional good judgment held on the collage of Amsterdam throughout the interval September 1990-May 1991. Modal good judgment, both as an issue or as a device, is usual to lots of the papers during this quantity. a few of the papers are con­ cerned with what could be referred to as recognized or conventional modal platforms, yet, as a brief look through this quantity will display, this on no account signifies that they stroll the crushed tracks. In­ deed, such contributions demonstrate new instructions, new effects, and new strategies to procure favourite effects. different papers during this quantity are consultant examples of a present pattern in modal common sense: the research of extensions or diversifications of the traditional sys­ tems which have been brought to beat a variety of shortcomings of the latter, specially their constrained expressive strength. ultimately, there's one other significant topic that may be discerned within the vol­ ume, a topic that could be defined through the slogan 'representing altering info. ' Papers falling below this heading deal with long-standing matters within the sector, or current a scientific technique, whereas a serious survey and a document contributing new suggestions also are incorporated. the majority of the papers on natural modal common sense care for theoreti­ calor even foundational points of modal systems.

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For example, we can combine the attribute PERSON with the atomic AVM 1st to form the AVM [PERSON 1st], and in this AVM we say that the attribute PERSON takes the value 1st. Third, any attribute and any AVM can be enclosed in that order between square brackets, and the result is another AVM. In short, attributes can take complex values. For example, [AGREEMENT [NUMBER plural]] is an AVM where the attribute AGREEMENT takes the complex value [NUMBER plural]. Finally, given a finite collection of non-atomic AVMs, a new AVM may be formed by enclosing the collection in square brackets, and then erasing the outermost brackets of the enclosed AVMs.

The first type of path equation equates a list of attributes with a value. For example, a user may write: (VP VERB HEAD NUM) = sing. The item between the angle brackets are attributes, and the item on the right hand side of the equality symbol is an atomic value. The meaning of this first type of path equation is that by making the sequence of transitions encoded by the list on the left, one will arrive at at a node bearing the atomic information sing. In short, this path equation bears the same information as the L wff (VP) (VERB) (HEAD) (NUM) sing, and more generally, this first type of path equation can be represented by means of L wffs.

Let's now consider what happens if we impose the three restrictions on the distribution of atomic information that many computational linguists make. First, if we want to forbid constantconstant clashes we add all instances of: (Gcc) Po: -+ -'P{3, for all a,{3 E A such that a =1= {3. The addition of these axioms obviously rules out constant-constant clashes in the Henkin model, and thus we have another completeness result. Second, to insist that atomic information is only instantiated at terminal nodes, we add as axioms all instances of: (Term) Po: -+ -,(l}T, for all a E A, and alll E £.

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