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43
Towards a Logic of Ambiguous Expressions
, 1996
"... this paper is as follows: in section 2 the possibility of a disjunctive approach to the meaning of ambiguous expressions will be discussed. Section 3 will sketch how the approach of this paper compares with other recent work on ambiguity. Sections 4 and 5 will present the semantics of a logical lang ..."
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Cited by 30 (3 self)
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this paper is as follows: in section 2 the possibility of a disjunctive approach to the meaning of ambiguous expressions will be discussed. Section 3 will sketch how the approach of this paper compares with other recent work on ambiguity. Sections 4 and 5 will present the semantics of a logical language containing ambiguous constants. Section 6 evaluates the resulting logics, and section 7 takes up some loose ends.
Specifying Who: On The Structure, Meaning, And Use Of Specificational Copular Clauses
, 2004
"... ..."
On the semantic readings of proofnets
 Proceedings of formal Grammar
, 1996
"... A la mémoire de ..."
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The Sasaki hook is not a [static] implicative connective but induces a backward [in time] dynamic one that assigns causes
 Int. Journ. of Theor. Physics
"... In this paper we argue that the Sasaki adjunction, which formally encodes the logicality that different authors tried to attach to the Sasaki hook as a ‘quantum implicative connective’, has a fundamental dynamic nature and encodes the socalled ‘causal duality ’ (Coecke, Moore and Stubbe 2001) for t ..."
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Cited by 11 (6 self)
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In this paper we argue that the Sasaki adjunction, which formally encodes the logicality that different authors tried to attach to the Sasaki hook as a ‘quantum implicative connective’, has a fundamental dynamic nature and encodes the socalled ‘causal duality ’ (Coecke, Moore and Stubbe 2001) for the particular case of a quantum measurement with a projector as corresponding selfadjoint operator. In particular: The action of the Sasaki hook (a S → −) for fixed antecedent a assigns to some property “the weakest cause before the measurement of actuality of that property after the measurement”, i.e. (a S → b) is the weakest property that guarantees actuality of b after performing the measurement represented by the projector that has the ‘subspace a ’ as eigenstates for eigenvalue 1, say, the measurement that ‘tests ’ a. From this we conclude that the logicality attributable to quantum systems contains a fundamentally dynamic ingredient: Causal duality actually provides a new dynamic interpretation of orthomodularity. We also reconsider the status of the Sasaki hook within ‘dynamic (operational) quantum logic ’ (DOQL), what leads us to the claim made in the title of this paper. More explicitly, although (as many argued in the past) the Sasaki hook should not be seen as an implicative hook, the formal motivation that persuaded others to do so, i.e. the Sasaki adjunction, does have a physical
Dynamic Modal Predicate Logic
, 1994
"... this paper is to combine within the same logic the dynamic account of variable binding from Groenendijk and Stokhof (1991a) with the dynamic account of epistemic updating from Veltman (1991), thus combining the useful features of Dynamic Predicate Logic (DPL) with those of Update Logic (UL). At the ..."
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Cited by 10 (7 self)
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this paper is to combine within the same logic the dynamic account of variable binding from Groenendijk and Stokhof (1991a) with the dynamic account of epistemic updating from Veltman (1991), thus combining the useful features of Dynamic Predicate Logic (DPL) with those of Update Logic (UL). At the end of the paper we will briefly look at further extensions along other scorekeeping dimensions. The DPL features provide a compositional treatment of anaphoric binding, while UL provides us with a treatment of epistemic modalities. By combining the two, our logic provides a suitable framework for the representation of natural language texts involving unbound anaphora and epistemic operators, and the interplay between those. Consider the following example texts. A man walked out. Maybe he was angry. (1) If a man walks out, then maybe he is angry. (2) The semantic analysis of these example texts poses a combination of two problems. The pronoun `he' must be linked to its antecedent; in the first example this is difficult because the antecedent is in a different sentence, while the second example poses the problem of getting the universal reading for the antecedent together with the intended anaphoric link. The adverb `maybe' intuitively acts as a consistency check on the piece of discourse that it has scope over. Its use in the two example texts above makes intuitive sense, but the next example illustrates that it can also serve to rule out anaphoric links. Maybe a man walked out.
CLASSICAL NONASSOCIATIVE LAMBEK CALCULUS
"... We introduce nonassociative linear logic, which may be seen as the classical version of the nonassociative Lambek calculus. We define its sequent calculus, its theory of proof nets, for which we give a correctness criterion and a sequentialization theorem, and we show proof search in it is polyno ..."
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Cited by 9 (1 self)
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We introduce nonassociative linear logic, which may be seen as the classical version of the nonassociative Lambek calculus. We define its sequent calculus, its theory of proof nets, for which we give a correctness criterion and a sequentialization theorem, and we show proof search in it is polynomial.
Monotonicity and Collective Quantification
"... This article studies the monotonicity behavior of plural determiners that quantify over collections. Following previous work, we describe the collective interpretation of determiners such as all, some and most using generalized quantifiers of a higher type that are obtained systematically by applyin ..."
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Cited by 6 (1 self)
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This article studies the monotonicity behavior of plural determiners that quantify over collections. Following previous work, we describe the collective interpretation of determiners such as all, some and most using generalized quantifiers of a higher type that are obtained systematically by applying a type shifting operator to the standard meanings of determiners in Generalized Quantifier Theory. Two processes of counting and existential quantification that appear with plural quantifiers are unified into a single determiner fitting operator, which, unlike previous proposals, both captures existential quantification with plural determiners and respects their monotonicity properties. However, some previously unnoticed facts indicate that monotonicity of plural determiners is not always preserved when they apply to collective predicates. We show that the proposed operator describes this behavior correctly, and characterize the monotonicity of the collective determiners it derives. It is proved that determiner fitting always preserves monotonicity properties of determiners in their second argument, but monotonicity in the first argument of a determiner is preserved if and only if it is monotonic in the same direction in the second argument. We argue that this asymmetry follows from the conservativity of generalized quantifiers in natural language.
Uniqueness of Normal Proofs in Implicational Intuitionistic Logic
 Journal of Logic, Language and Information
, 1999
"... . A minimal theorem in a logic L is an Ltheorem which is not a nontrivial substitution instance of another Ltheorem. Komori (1987) raised the question whether every minimal implicational theorem in intuitionistic logic has a unique normal proof in the natural deduction system NJ. The answer has be ..."
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Cited by 5 (0 self)
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. A minimal theorem in a logic L is an Ltheorem which is not a nontrivial substitution instance of another Ltheorem. Komori (1987) raised the question whether every minimal implicational theorem in intuitionistic logic has a unique normal proof in the natural deduction system NJ. The answer has been known to be partially positive and generally negative. It is shown here that a minimal implicational theorem A in intuitionistic logic has a unique finormal proof in NJ whenever A is provable without nonprime contraction. The nonprime contraction rule in NJ is the implication introduction rule whose cancelled assumption differs from a propositional variable and appears more than once in the proof. Our result improves the known partial positive solutions to Komori's problem. Also, we present another simple example of a minimal implicational theorem in intuitionistic logic which does not have a unique fijnormal proof in NJ. Key words: natural deduction, uniqueness of normal proofs, coh...