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.

A la mémoire de

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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 score-keeping 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.

We introduce non-associative linear logic, which may be seen as the classical version of the non-associative 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.

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 so-called ‘causal duality ’ (Coecke, Moore and Stubbe 2001) for the particular case of a quantum measurement with a projector as corresponding self-adjoint 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

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We prove that the Lambek calculus is complete w.r.t. L-models, i.e., free semigroup models. We also prove the completeness w.r.t. relativized relational models over the natural linear order of integers.

Modern logic is often defined in terms of specific formal languages, rules, and calculi. Such architectural decisions about a field form a pervasive implicit definition which determines professional practice -- through the structure of textbooks, as well as the research agenda that determines 'interest', and hence acceptance and academic status. Such a practice may come to contain a lot of historical accident, or force of habit. Therefore, it seems worth thinking about the defining agenda of a field once in a while. In this brief essay, we explore alternative views of logic, locating the nature of the field in more abstract themes, concerns and attitudes. The new definition does not remove the need for the old agenda, but we advocate a shift in emphasis, toward greater generality and range of application. The outcome is a conception of logic as a broad methodological stance, looking for invariants in (information) structures and processes. to appear in A. Varzi, ed. "The European Revie...

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