A new system of dynamic logic is introduced and motivated, witha novel approach to variable binding for incremental interpretation. Thesystem is shown to be equivalent to first order logic and complete.The new logic combines the dynamic binding idea from DynamicPredicate Logic with De Bruijn style variable free indexing. Quantifiersbind the next available variable register; the indexing mechanismguarantees that active registers are never overwritten by newquantifiers actions. Apart from its interest in its own right, theresulting system has certain advantages over Dynamic (...) Predicate Logic orDiscourse Representation Theory. It comes with a more well behaved(i.e., transitive) consequence relation, it gives a more explicitaccount of how anaphoric context grows as text gets processed, and ityields new insight into the dynamics of anaphoric linking in reasoning.Incremental dynamics also points to a new way of handling contextdynamically in Montague grammar. (shrink)

Relational Grammar (RG) was introduced in the 1970s as a theory of grammatical relations and relation change, for example, passivization, dative shift, and raising. Furthermore, the idea behind RG was that transformations as originally designed in generative grammar were unable to capture the common kernel of, e.g., passivization across languages. The researchconducted within RG has uncovered a wealth of phenomena for which it could produce a satisfactory analysis. Although the theory of Government and Binding has answered some of the complaints, (...) still it left many phenomena unaccounted for. Referent Systems (RSs) have been introduced by Vermeulen (1995) to overcome certain weaknesses of Dynamic Semantics. Their usefulness has not yet been realized in semantical theory. We shall show here that their significance cannot be overestimated. Namely, we will show in this paper that there exists a fundamental affinity to RG. Both handle the relation between an argument and a functor by means of a shared relational sign, which is unique for each argument. This assignment can be changed. What is interesting is that the notion of a chômeur, which is central to RG, finds a natural treatment in RSs. This coincidence is in our view not accidental but reveals some fundamental properties of the human language faculty. (shrink)

The present paper is the result of a long struggle to understand how the notion of compositionality can be used to motivate the structure of a sentence. While everyone seems to have intuitions about which proposals are compositional and which ones are not, these intuitions generally have no formal basis. What is needed to make such arguments work is a proper understanding of what meanings are and how they can be manipulated. In particular, we need a definition of meaning that (...) bans all mentioning of syntactic structure; it is not the task of semantics to state in which way things are put together in syntax. The present paper presents such a theory of meaning. This, in tandem with some minimal assumptions on the syntactic process (that there can be no deletion) yield surprisingly deep insights into natural language. First, it rehabilitates a lot of linguistic work as necessary on semantic grounds and defends it against potential claims of redundancy. For example, θ-roles and linking are an integral part of semantics, and not syntax. To assume the latter is to put the cart before the horse. Second, as a particular example we shall show that Dutch is not strongly context free even if weakly context free. To our knowledge, this is the first formal proof of this fact. (shrink)

The paper sets out to offer an alternative to the function/argument approach to the most essential aspects of natural language meanings. That is, we question the assumption that semantic completeness (of, e.g., propositions) or incompleteness (of, e.g., predicates) exactly replicate the corresponding grammatical concepts (of, e.g., sentences and verbs, respectively). We argue that even if one gives up this assumption, it is still possible to keep the compositionality of the semantic interpretation of simple predicate/argument structures. In our opinion, compositionality presupposes (...) that we are able to compare arbitrary meanings in term of information content. This is why our proposal relies on an ‘intrinsically’ type free algebraic semantic theory. The basic entities in our models are neither individuals, nor eventualities, nor their properties, but ‘pieces of evidence’ for believing in the ‘truth’ or ‘existence’ or ‘identity’ of any kind of phenomenon. Our formal language contains a single binary non-associative constructor used for creating structured complex terms representing arbitrary phenomena. We give a finite Hilbert-style axiomatisation and a decision algorithm for the entailment problem of the suggested system. (shrink)

This paper develops a semantics with control over scope relations using Vermeulen’s stack valued assignments as information states. This makes available a limited form of scope reuse and name switching. The goal is to have a general system that fixes available scoping effects to those that are characteristic of natural language. The resulting system is called Scope Control Theory, since it provides a theory about what scope has to be like in natural language. The theory is shown to replicate a (...) wide range of grammatical dependencies, including options for, and constraints on, ‘donkey’, ‘binding’, ‘movement’, ‘Control’ and ‘scope marking’ dependencies. (shrink)

Combining logics has become a rapidly expanding enterprise that is inspired mainly by concerns about modularity and the wish to join together tailor made logical tools into more powerful but still manageable ones. A natural question is whether it offers anything new over and above existing standard languages. By analysing a number of applications where combined logics arise, we argue that combined logics are a potentially valuable tool in applied logic, and that endorsements of standard languages often miss the point. (...) Using the history of quantified modal logic as our main example, we also show that the use of combined structures and logics is a recurring theme in the analysis of existing logical systems. (shrink)