| J. van Benthem. Essays in Logical Semantics. D. Reidel, Dordrecht, 1986. |
....mechanism for such an ability seems to be compositionality. Situation semantics closes another gap of traditional semantic approaches: the neglect of subject matter and partiality of information. In traditional semantics, statements which are true in the same models convey the same information [13]. Situation semantics takes the view that logically equivalent sentences need not have the same subject matter, they need not describe situations involving the same object and properties. The notion of partial situations (partial models) leads to a more fine grained notion of information content ....
J. van Benthem. Essays in Logical Semantics, Dordrecht, Holland: Reidel, 1986.
....[13, 14] combine signs such as the ones in (1) with the help of the undirected Lambek Calculus, our signs will be combined using linear combinators. Mathematically this boils down to the same thing, as proofs in the undirected Lambek Calculus are in 1 1 correspondence with the latter (Van Benthem [1, 2, 3]) But a move from proofs to combinators spares the working linguist much technical overhead and it will serve our purpose to stress the point that semantics need not be dependent on any form of syntax. A second divergence from Oehrle s work is that we move from terms over structures (strings ....
J.F.A.K. van Benthem. Essays in Logical Semantics. Reidel, Dordrecht, 1986.
....one would like is a property, say P, which implies monotonicity and is such that ( If Q is a monotone NL quanti er, then Q has P. We now propose such a property; it was introduced by van Benthem and applied by him to various aspects of the computational behavior of quanti ers (cf. van Benthem [3]) but not as far as we know in the present context. 16 De nition 19 A function f : N N such that f(n) n 1 is smooth if, for all n, f(n) f(n 1) f(n) 1: Also, Q f and Q rel f are called smooth if f is smooth. As we stated in the universal (U 3 ) section 1.3) it appears that all ....
van Benthem, J., 1986. Essays in Logical Semantics, D. Reidel, Dordrecht.
.... can be sensitive to word order while retaining the hypothetical reasoning capabilities of standard (commutative) linear logic that make it so well adapted to handling such phenomena as quantifier scoping [2] Some connections between the Lambek calculus and group structure have long been known [9], and linear logic itself has some aspects strongly reminiscent of groups (the producer consumer duality of a formula A with its 1 linear negation A ) but no serious attempt has been made so far to base a theory of linguistic description solely on group structure. This paper presents such a ....
Johan van Benthem. Essays in Logical Semantics. D. Reidel, Dordrecht, Holland, 1986. 17
.... can be sensitive to word order while retaining the hypothetical reasoning capabilities of standard (commutative) linear logic that make it so well adapted to handling such phenomena as quantifier scoping [4] Some connections between the Lambek calculus and group structure have long been known [16], and linear logic itself has some aspects strongly reminiscent of groups (the producer consumer duality of a formula A with its linear negation A ) but no serious attempt has been made so far to base a theory of linguistic description solely on group structure. This paper presents such a ....
van Benthem, J.: 1986, Essays in Logical Semantics. Dordrecht, Holland: D. Reidel.
....and also non commutative. They are also intuitionistic, but this is more standard, especially in computational logic. The revival of interest in these calculi is mainly due to advances in logic. First van Benthem and Moortgat enriched them with modalities and used techniques from modal logic [93, 95, 62] and also [64] with a slightly different approach. Nevertheless 4 the relation to other logics, in particular with intuitionistic logic and classical logic has only been clarified with the invention of linear logic by Girard [30] the full power of intuitionistic logic is recovered by modalities ....
Johan van Benthem. Essays in Logical Semantics. Reidel, Dordrecht, 1986.
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J. van Benthem. Essays in Logical Semantics. D. Reidel, Dordrecht, 1986.
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Van Benthem, J.F.A.K.: 1986, Essays in Logical Semantics, Reidel, Dordrecht.
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