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**11 - 16**of**16**### Type Logical Grammar: Categorial Logic of Signs

, 1994

"... tracting away from contingent aspects of the channel's physical realization and from the use of the information by the recipient. For instance, the finiteness of language processors demands that the meanings of sufficiently complex signs be a function of the meanings of their parts: thus compos ..."

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tracting away from contingent aspects of the channel's physical realization and from the use of the information by the recipient. For instance, the finiteness of language processors demands that the meanings of sufficiently complex signs be a function of the meanings of their parts: thus compositionality. Without additional constraints, compositionality could be trivially satisfied (Zadrozny 1994). But the fact that language users derive their implicit contract for sign meaning from finite evidence imposes strong uniformity requirements on signs. While this argument has not, to my knowledge, been made rigorous through an axiomatic treatment, type-logical grammar offers a promising notion of uniformity: to say, for instance, that a sign c meaning z has type B/A is to say that c + a (where + is a suitable sign combination operator) has type B and means z(x), given that a has type A and means x. But uniformity must also go backwards, if the use and meaning of a sign is to be induced from

### aspert i&s. unibo. it

"... We analyze the inherent complexity of implementing L&y’s notion of optimal evaluation for the &calculus, where similar redexes are contracted in one step via so-called parallel /%rekction. optimal evaluation IQSS finally realized by Lamping, who introduced a beautiful graph reduction technol ..."

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We analyze the inherent complexity of implementing L&y’s notion of optimal evaluation for the &calculus, where similar redexes are contracted in one step via so-called parallel /%rekction. optimal evaluation IQSS finally realized by Lamping, who introduced a beautiful graph reduction technology for sharing evaluation. contexts dual to the sharing of values. His pioneering insights have been modified and improved in subsequent implementations of optimal reduction. We prove that the cost of parallel P-reduction is not bounded by any ICalm&-elementary recursive function. Not merely do we establish that the parallel

### Consistency Preserving Updates: Extended Abstract

"... N. Bidoit, S. Cerrito, Ch. Froidevaux 1 1 Introduction The concern in this paper is to formalize update under transition constraints in an incomplete information setting. A wide variety of proposals for formalizing database (knowledge base) update semantics exists (e.g. [9] [11] [15] [4] [12] [13 ..."

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N. Bidoit, S. Cerrito, Ch. Froidevaux 1 1 Introduction The concern in this paper is to formalize update under transition constraints in an incomplete information setting. A wide variety of proposals for formalizing database (knowledge base) update semantics exists (e.g. [9] [11] [15] [4] [12] [13]). In this paper we investigate a substantially different proposal exploiting some features of linear logic [7]. Our aim is to provide a mechanism to perform updates such that if we start with a "consistent database" then the result of an update is a new database which is always "consistent". The database is specified by three kinds of information : ffl Atomic facts : intuitively, the database stores explicitly two kinds of facts, true ones and false ones. We deal with incomplete information in a very simple and naive way, that is, for an information (proposition) A, if neither A nor the negation of A is stored then A has the status unknown. ffl Deduction rules : we deal with two kinds o...