Time adverbials introduced by until impose restrictions on the aspectual class of the main clause they combine with: they only combine with durative sentences. In negative sentences, the situation is more complex. The question arises whether negative sentences are durative, or whether there is a separate use of until as a negative polarity item. In this paper, I discuss the three treatments of not…until that are characterized in the literature as the scope analysis, the ambiguity thesis and the lexical composition (...) approach. I work out the interpretation of the three approaches in an event-based semantics, and argue that they are truth-conditionally equivalent in sentences containing an explicit negation. Furthermore, they generate the same pragmatic implicatures. A seperate negative polarity use of until is motivated by sentences containing NPI-licensers different from explicit negation, though. The observation that the scope analysis, the ambiguity thesis and the lexical composition approach are semantically and pragmatically equivalent in sentences containing an explicit negation helps us describe the similarities and differences between the expression of exclusion of a range of values on the time axis in a variety of languages. (shrink)
This paper addresses the two interpretations that a combination ofnegative indefinites can get in concord languages like French:a concord reading, which amounts to a single negation, and a doublenegation reading. We develop an analysis within a polyadic framework,where a sequence of negative indefinites can be interpreted as aniteration of quantifiers or via resumption. The first option leadsto a scopal relation, interpreted as double negation. The secondoption leads to the construction of a polyadic negative quantifiercorresponding to the concord reading. Given that (...) sentential negationparticipates in negative concord, we develop an extension of thepolyadic approach which can deal with non-variable binding operators,treating the contribution of negation in a concord context assemantically empty. Our semantic analysis, incorporated into agrammatical analysis formulated in HPSG, crucially relies on theassumption that quantifiers can be combined in more than one wayupon retrieval from the quantifier store. We also considercross-linguistic variation regarding the participation ofsentential negation in negative concord. (shrink)
This paper addresses the two interpretations that a combination ofnegative indefinites can get in concord languages like French:a concord reading, which amounts to a single negation, and a doublenegation reading. We develop an analysis within a polyadic framework,where a sequence of negative indefinites can be interpreted as aniteration of quantifiers or via resumption. The first option leadsto a scopal relation, interpreted as double negation. The secondoption leads to the construction of a polyadic negative quantifiercorresponding to the concord reading. Given that (...) sentential negationparticipates in negative concord, we develop an extension of thepolyadic approach which can deal with non-variable binding operators,treating the contribution of negation in a concord context assemantically empty. Our semantic analysis, incorporated into agrammatical analysis formulated in HPSG, crucially relies on theassumption that quantifiers can be combined in more than one wayupon retrieval from the quantifier store. We also considercross-linguistic variation regarding the participation ofsentential negation in negative concord. (shrink)
This paper develops an analysis of the temporal role of negative sentences in narrative discourse in English and French. The analysis focuses on differences in the aspectual systems of English and French, and their consequences for the interpretation of negation and quantification. A recursive rule for the introduction of discourse referents characterizes both quantificational and negated sequences as complex states. The notion of coercion explains why states (including complex states) can behave as events at the level of narrative discourse. The (...) analysis is implemented in the framework of Discourse Representation Theory (DRT) developed by Kamp & Reyle (1993). (shrink)
Having studied mathematics, in particular foundations and philosophy of mathematics, it happened that I was asked to teach logic to the students in the Faculty of Philosophy of the Radboud University Nijmegen. It was there that I discovered that logic is much more than just a mathematical discipline consisting of definitions, theorems and proofs, and that logic can and should be embedded in a philosophical context. After ten years of teaching logic at the Faculty of Philosophy at the Radboud University (...) Nijmegen, thirty years at the Faculty of Philosophy of Tilburg University and nine years at the Faculty of Philosophy of the Erasmus University Rotterdam, I got many ideas how to improve my LOGIC book which was published twenty five years ago in 1993 by Verlag Peter Lang. Although the amount of work was enormous, I felt I should do it. It is like working on a large painting where you put some extra color in one corner, add a little detail at another place, shed some more light on a particular face, etc. (shrink)
In this article, we model FPTP systems as social preference rules and give two characterizations. We show that a social preference rule is an FPTP system if, and only if, it satisfies the axioms of subset consistency, district consistency, subset cancellation, and district cancellation. The second characterization consists of the axioms of subset consistency, subset anonymity, neutrality, topsonlyness, Pareto optimality, district consistency and district cancellation. The characterizations give us an opportunity to compare the characteristic properties of FPTP systems to the (...) characteristic properties that we found for list systems of proportional representation (list PR systems) in Hout et al. (Social Choice and Welfare, 27:459–475, 2006), where we modelled those systems also as social preference rules. We find that consistency and anonymity distinguish list PR systems from FPTP systems. On the other hand, it is district cancellation that distinguishes FPTP systems from list PR systems. (shrink)
This paper discusses the characteristic properties of List PR systems and FPTP systems, as given in Hout 2005 and Hout et al. 2006. While many of the properties we consider are common to both systems, it turns out that the British system distinguishes itself by satisfying the district cancel lation property, while the Dutch system distinguishes itself by satisfying consistency and anonymity. For scoring rules, topsonlyness is equivalent to being party fragmentation-proof . One might present this as an argument in (...) favour of requiring topsonlyness. However, we will also give counter-arguments against insisting upon the property of being party fragmentation-proof. (shrink)
Depending on what one means by the main connective of logic, the -if..., then... -, several systems of logic result: classic and modal logics, intuitionistic logic or relevance logic. This book presents the underlying ideas, the syntax and the semantics of these logics. Soundness and completeness are shown constructively and in a uniform way. Attention is paid to the interdisciplinary role of logic: its embedding in the foundations of mathematics and its intimate connection with philosophy, in particular the philosophy of (...) language. Set theory is presented both as a conditio sine qua non for logic and as a interesting exact ontology. The study of infinite sets yields perplexing results. Formalization of informal number theory results in formal number theory; Godel's incompleteness is treated. At appropriate places attention is paid to paradoxes, intuitionism, conditionals, the historical development of logic, to logic programming and automated theorem proving for classical logic.". (shrink)
The neutralization of contrasts in form or meaning that is sometimes observed in language production and comprehension is at odds with the classical view that language is a systematic one-to-one pairing of forms and meanings. This special issue is concerned with patterns of forms and meanings in language. The papers in this special issue arose from a series of workshops that were organized to explore variants of bidirectional Optimality Theory and Game Theory as models of the interplay between the speaker’s (...) and the hearer’s perspective. (shrink)
We introduce an implication-with-possible-exceptions and define validity of rules-with-possible-exceptions by means of the topological notion of a full subset. Our implication-with-possible-exceptions characterises the preferential consequence relation as axiomatized by Kraus, Lehmann and Magidor [Kraus, Lehmann, and Magidor, 1990]. The resulting inference relation is non-monotonic. On the other hand, modus ponens and the rule of monotony, as well as all other laws of classical propositional logic, are valid-up-to-possible exceptions. As a consequence, the rules of classical propositional logic do not determine the (...) meaning of deducibility and inference as implication-without-exceptions. (shrink)
We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logicalnotions considered we suggest that the "most natural" reading is precisely the one which is required by the recent intuitionistic completeness theorems for IPC.
This volume is an outgrowth of the second Workshop on Logic, Language and Computation held at Stanford in the spring of 1993. The workshop brought together researchers interested in natural language to discuss the current state of the art at the borderline of logic, linguistics and computer science. The papers in this collection fall into three central research areas of the nineties, namely quantifiers, deduction, and context. Each contribution reflects an ever-growing interest in a more dynamic approach to meaning, which (...) focuses on inference patterns and the interpretation of sentences in the context of a larger discourse. The papers apply either current logical machinery - such as linear logic, generalised quantifier theory, dynamic logic - or formal analyses of the notion of context in discourse to classical linguistic issues, with original and thought-provoking results deserving of a wide audience. (shrink)
Intuitionistically. a set has to be given by a finite construction or by a construction-project generating the elements of the set in the course of time. Quantification is only meaningful if the range of each quantifier is a well-circumscribed set. Thinking upon the meaning of quantification, one is led to insights?in particular, the so-called continuity principles?which are surprising from a classical point of view. We believe that such considerations lie at the basis of Brouwer?s reconstruction of mathematics. The predicate ?α (...) is lawless? is not acceptable, the lawless sequences do not form a well-circumscribed intuitionistic set, and quantification over lawless sequences does not make sense. (shrink)
This paper addresses the two interpretations that a combination ofnegative indefinites can get in concord languages like French:a concord reading, which amounts to a single negation, and a doublenegation reading. We develop an analysis within a polyadic framework,where a sequence of negative indefinites can be interpreted as aniteration of quantifiers or via resumption. The first option leadsto a scopal relation, interpreted as double negation. The secondoption leads to the construction of a polyadic negative quantifiercorresponding to the concord reading. Given that (...) sentential negationparticipates in negative concord, we develop an extension of thepolyadic approach which can deal with non-variable binding operators,treating the contribution of negation in a concord context assemantically empty. Our semantic analysis, incorporated into agrammatical analysis formulated in HPSG, crucially relies on theassumption that quantifiers can be combined in more than one wayupon retrieval from the quantifier store. We also considercross-linguistic variation regarding the participation ofsentential negation in negative concord. (shrink)
