Download Modality, Semantics and Interpretations: The Second Asian by Shier Ju, Hu Liu, Hiroakira Ono PDF

By Shier Ju, Hu Liu, Hiroakira Ono

This contributed quantity contains either theoretical examine on philosophical common sense and its functions in synthetic intelligence, in most cases utilizing the ideas and methods of modal good judgment. It collects chosen papers offered on the moment Asia Workshop on Philosophical common sense, held in Guangzhou, China in 2014, in addition to a few invited papers by way of experts in similar fields. The contributions characterize pioneering philosophical good judgment study in Asia.

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Extra info for Modality, Semantics and Interpretations: The Second Asian Workshop on Philosophical Logic

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The ‘only if’ part of (I), for S not containing (i), is proved by induction on cut-free proofs in FNL∗S . 1 and (CUT). ⊥) or (a. ), then N ( ) ⇒ P(γ) is also an axiom from this group. The rules for ∧, ∨ and (L ·), (R\), (R/) are treated easily. Let us consider (L∨). By the induction hypothesis, N ( [α]) ⇒ P(γ) and N ( [β]) ⇒ P(γ). Then, N ( )[N (α)] ⇒ P(γ) and N ( )[N (β)] ⇒ P(γ), and we apply (L∨) in FNL S . Structural rules (a), (e), (c) cause no problem: the induction hypothesis applied to the premise directly yields our claim for the conclusion.

If U, V are sets of formulae and ◦ is a binary connective, then we define: U ◦ V = {α ◦ β : α ∈ U, β ∈ V }. Every formula γ in language (·, \, /, ∧, ∨) is translated into a set I (γ), of formulae in language (·, \, /). This also works with 1, 0, ⊥, added to both languages. 3) 37 I (α) = {α}, for any atomic formula α, I (α ◦ β) = I (α) ◦ I (β), for ◦ ∈ {·, \, /}, I (α ◦ β) = I (α) ∪ I (β), for ◦ ∈ {∧, ∨}. The occurrence of a connective ◦ in a formula (resp. sequent) is called positive, if ◦ is the main connective of a subformula which occurs positively in this formula (resp.

We give a few examples. Let us fix the atomic types: s (sentence), n (proper noun), cn (common noun). α\β (resp. β/α) is interpreted as the type of functors (or: functional expressions) which with any expression of type α on the left (resp. right) form a compound expression of type β. g. ‘some,’ ‘every,’ ‘one,’ cn/cn of adjective (as noun modifier), (cn/cn)/(cn/cn) of adverb (as adjective modifier), and so on. This typing is by no way the only possible option. Different authors propose different types.

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