Mark Hepple. Hybrid Categorial Logics. Logic Journal of the IGPL, 3(2,3), 343--355, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....have to find a proof format where the structure of the antecedent database is gradually discovered in the proof process. 10 In the categorial literature, a variety of labelled sequent formulations have been proposed for this purpose see, among others, Moortgat 92, Oehrle 95, Morrill 94, Hepple 95] One considers labelled sequents x 1 : A 1 , x n : An # t : B where the antecedent is simply a multiset of labelled formulae, representing the lexical assumptions (seen as occurrences, i.e. with the x i distinct) and where t is a structure label built from these x i by means of the ....

....theory for the multimodal systems, we now complement the Curry Howard labelling with a system of structure labeling, that serves the same purpose as the antecedent structuring in the (labelled) Natural Deduction presentation of Def 2.3. The labeling regime of Def 3. 4 is related to proposals in [Hepple 95, Morrill 95, Oehrle 95] but makes adjustments to accommodate the multimodal architecture in its full generality. Definition 3.4 Structure labels: syntax. The labeling system uses atomic formula labels x and structure labels ###, # # #) forthe# formula decomposition nodes. For the # ....

Mark Hepple. Hybrid Categorial Logics. Logic Journal of the IGPL, 3(2,3), 343--355, 1995.

....A . B # A# B. This perspective is taken in general terms in [Moortgat Oehrle 93] where two products . i and . j are related by an inclusion principle A . i B # A . j B if the latter has greater freedom of resource management than the former. The opposite view is taken in [Hepple 95] where one finds a systematic reversal of the derivability arrows in the inclusion principles, e.g. A# B # A . B. In [Kurtonina 95] it is shown that from the frame semantics point of view the two perspectives can be equally well accommodated: they reflect the choice for a conjunctive ....

Hepple, M. (1995), `Hybrid Categorial Logics'. Bulletin of the IGPL 3(2,3). Special issue on Deduction and Language (ed. R. Kempson), 343--355.

....we have to nd a proof format where the structure of the antecedent database is gradually discovered in the proof process. 10 In the categorial literature, a variety of labelled sequent formulations have been proposed for this purpose see, among others, Moortgat 92, Oehrle 95, Morrill 94, Hepple 95] One considers labelled sequents x 1 : A 1 ; xn : An ) t : B where the antecedent is simply a multiset of labelled formulae, representing the lexical assumptions (seen as occurrences, i.e. with the x i distinct) and where t is a structure label built from these x i by means of the ....

....theory for the multimodal systems, we now complement the Curry Howard labelling with a system of structure labeling, that serves the same purpose as the antecedent structuring in the (labelled) Natural Deduction presentation of Def 2.3. The labeling regime of Def 3. 4 is related to proposals in [Hepple 95, Morrill 95, Oehrle 95] but makes adjustments to accommodate the multimodal architecture in its full generality. De nition 3.4 Structure labels: syntax. The labeling system uses atomic formula labels x and structure labels h i; for the 8 formula decomposition nodes. For the 9 nodes, we ....

Mark Hepple. Hybrid Categorial Logics. Logic Journal of the IGPL, 3(2,3), 343-355, 1995.

....formulas is unproblematic. It comprises a set with just two primitives combined within a logical system whose only connective is (and possibly : Such a system is familiar an impoverished relative of much richer current categorial systems [Morrill 1994, Moortgat 1995, Hepple 1990, Hepple 1995] The language of the labelling algebra is however extremely heterogeneous. A quantifier free predicate logic expresses concepts associated with natural language expressions. But there are a number of additional features of this labelling language, none of which is unproblematic. Firstly, there ....

Hepple, M. Hybrid Categorial Logics. IGPL Vo.3 Nos.2-3, pp.343-55.

....A ffl B A Omega B. This perspective is taken in general terms in [Moortgat Oehrle 93] where two products ffl i and ffl j are related by an inclusion principle A ffl i B A ffl j B if the latter has greater freedom of resource management than the former. The opposite view is taken in [Hepple 95] where one finds a systematic reversal of the derivability arrows in the inclusion principles, e.g. A Omega B A ffl B. In [Kurtonina 95] it is shown that from the frame semantics point of view the two perspectives can be equally well accommodated: they reflect the choice for a conjunctive ....

Hepple, M. (1995), `Hybrid Categorial Logics'. Bulletin of the IGPL 3(2,3). Special issue on Deduction and Language (ed. R. Kempson), 343--355.

....The language needed to define the type logical formulas is unproblematic. It comprises a set with just two primitives combined within a logical system whose only connective is # (and possibly : Such a system is familiar an impoverished relative of much richer current categorial systems [33, 31, 16, 15]. The language of the labelling algebra is however extremely heterogeneous. A quantifier free predicate logic expresses concepts associated with natural language expressions. But there are a number of additional features of this labelling language, none of which is unproblematic. Firstly, there ....

Hepple, M. Hybrid Categorial Logics. IGPL Vo.3 Nos.2-3, pp.343-55.

....we have to find a proof format where the structure of the antecedent database is gradually discovered in the proof process. In the categorial literature, a variety of labelled sequent formulations have been proposed for this purpose, see, among others, Moortgat 92, Oehrle 95, Morrill 94, Hepple 95] One considers labelled sequents x 1 : A 1 ; xn : An ) t : B where the antecedent is simply a multiset of labelled formulae, representing the lexical assumptions (seen as occurrences, i.e. with the x i distinct) and where t is a structure label built from these x i by means of the ....

....have been studying in this paper. Below, we complement the Curry Howard labelling with a system of structure labeling, that serves the same purpose as the antecedent structuring in the (labelled) Natural Deduction presentation of Def 2.3. The labeling regime of Def 3. 5 is related to proposals in [Hepple 95, Morrill 95, Oehrle 95] but makes adjustments for the full multimodal architecture. Definition 3.5. Structure labels: syntax. The labeling system uses atomic formula labels x and structure labels hoei; oe ffi ) for the 8 formula decomposition nodes. For the 9 nodes, we use difference ....

Hepple, M. (1995), `Hybrid Categorial Logics'. Bulletin of the IGPL 3(2,3). Special issue on Deduction and Language (ed. R. Kempson), 343--355.

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Hepple, M. to appear. Hybrid Categorial Logics. Proceedings of Deduction and Language Workshop. Special edition of the Bulletin of the Interest Group in Pure and Applied Logics. Konig, E. 1990. `The complexity of parsing with extended categorial grammars', Proc. of COLING--90.

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