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Published byCarlos McPherson Modified over 3 years ago

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now the extensions…

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NL: a pure logic of residuation Axiom Transitivity Residuation

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Lambek calculus (sequents)

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+ modalities If brings you an A, then when provided with the structure S, it gives you an A with the structure S If with S brings you an A, then without it it gives you an A which lacks S!

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consequences [] A A ([] A) A A L [] L A [] A (A) A A [] R R

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+ structural postulates Example :

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Example: non peripheral extraction (that I met _ yesterday) nnnn nnnn nnnn npsss s P s ss s P sss s L sss s sss s ss)\) s ),/\(,((nn)\( \\ \ []/)\),/)\(,(( 2 )[]),\ /)\(,((( 1 )\),[]),/)\(,((( )\)),[],/)\((, )\)),,/)\((,.... nn\ nps),[]//(

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Example: non peripheral extraction (that I met _ yesterday) nnnn nnnn nnnn npsss s P s ss s P sss s L sss s sss s ss)\) s ),/\(,((nn)\( \\ \ []/)\),/)\(,(( 2 )[]),\ /)\(,((( 1 )\),[]),/)\(,((( )\)),[],/)\((, )\)),,/)\((,.... nn\ nps),[]//(

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Example: non peripheral extraction (that I met _ yesterday) nnnn nnnn nnnn P snpss s P sss s L sss s sss s ss)\) s ),/\(,((nn)\( \\ \,)ss\nps ),/)\((( 2 )[]),\ /)\(,((( 1 )\),[]),/)\(,((( )\)),[],/)\((, )\)),,/)\((,.... nn\ nps),[]//( s/ np[]

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Example: non peripheral extraction (that I met _ yesterday) nnnn nnnn nnnn P sssnps P sss s L sss s sss s ss)\) s ),/\(,((nn)\( \\ \,)ss\nps ),/)\((( 2 )),\ /)\(,((( 1 )\),[]),/)\(,((( )\)),[],/)\((, )\)),,/)\((,.... nn\ nps),[]//( s/ np[] np[]

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Example: non peripheral extraction (that I met _ yesterday) nnnn nnnn nnnn P sssnps P sss s L sss s sss s ss)\) s ),/\(,((nn)\( \\ \,)ss\nps ),/)\((( 2 )),\ /)\(,((( 1 )\), /)\(,((( )\)),[],/)\((, )\)),,/)\((,.... nn\ nps),[]//( s/ np[] np[] np[]

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Example: non peripheral extraction (that I met _ yesterday) nnnn nnnn nnnn P sssnps P sss s L sss s sss s ss)\) s ),/\(,((nn)\( \\ \,)ss\nps ),/)\((( 2 )),\ /)\(,((( 1 )\),),,/)\(,(((((( )\)),)),[],/)\(,( )\)),,/)\((,.... nn\ nps),[]//( s/ np[] np[] np[] )

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Example: non peripheral extraction (that I met _ yesterday) nnnn nnnn nnnn P sssnps P sss s L sss s sss s ss)\) s ),/\(,((nn)\( \\ \,)ss\nps ),/)\((( 2 )),\ /)\(,((( 1 )\),),,/)\(,(((((( )\)),)),[],/)\(,( )\)),,/)\((,.... nn\ nps),[]//( s/ np[] np[] np[] )

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Example: non peripheral extraction (that I met _ yesterday) nnnn nnnn nnnn P sssnps P sss s L sss s sss s ss)\) s ),/\(,((nn)\( \\ \,)ss\nps ),/)\((( 2 )),\ /)\(,((( 1 )\),),,/)\(,(((((( )\)),)),[],/)\(,( )\)),,/)\((,.... nn\ nps),[]//( s/ np[] np[] np[] )

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adapted proof-nets To take restructuring of resources into account To represent modalities see Richard Moots thesis –« Proof Nets for Linguistic Analysis »

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Uses a contraction criterion (graph- rewriting)

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a/a

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a a

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a a a a

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a a a a a a

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a a a a a a

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a a a a a a

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a a a a restructuring-1

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a/a a a restructuring-2

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a/a a contraction step

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