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30
Fresh Logic
 Journal of Applied Logic
, 2007
"... Abstract. The practice of firstorder logic is replete with metalevel concepts. Most notably there are metavariables ranging over formulae, variables, and terms, and properties of syntax such as alphaequivalence, captureavoiding substitution and assumptions about freshness of variables with resp ..."
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Cited by 219 (28 self)
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Abstract. The practice of firstorder logic is replete with metalevel concepts. Most notably there are metavariables ranging over formulae, variables, and terms, and properties of syntax such as alphaequivalence, captureavoiding substitution and assumptions about freshness of variables with respect to metavariables. We present oneandahalfthorder logic, in which these concepts are made explicit. We exhibit both sequent and algebraic specifications of oneandahalfthorder logic derivability, show them equivalent, show that the derivations satisfy cutelimination, and prove correctness of an interpretation of firstorder logic within it. We discuss the technicalities in a wider context as a casestudy for nominal algebra, as a logic in its own right, as an algebraisation of logic, as an example of how other systems might be treated, and also as a theoretical foundation
Conventional Signalling Acts and Conversation
"... This article aims to provide foundations for a new approach to Agent Communication Languages (ACLs). First, we outline the theory of signalling acts. In contrast to current approaches to communication, this account is neither intentionbased nor commitmentbased, but conventionbased. Next, we o ..."
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Cited by 14 (2 self)
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This article aims to provide foundations for a new approach to Agent Communication Languages (ACLs). First, we outline the theory of signalling acts. In contrast to current approaches to communication, this account is neither intentionbased nor commitmentbased, but conventionbased. Next, we outline one way of embedding that theory within an account of conversation. We move here from an account of the basic types of communicative act (the statics of communication) to an account of their role in sequences of exchanges in communicative interaction (the dynamics of communication). Finally, we apply the framework to the analysis of a conversational protocol.
Zooming in, zooming out
 JOURNAL OF LOGIC, LANGUAGE AND INFORMATION
, 1996
"... This is an exploratory paper about combining logics, combining theories and combining structures. Typically when one applies logic to such areas as computer science, artificial intelligence or linguistics, one encounters hybrid ontologies. The aim of this paper is to identify plausible strategies fo ..."
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Cited by 11 (1 self)
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This is an exploratory paper about combining logics, combining theories and combining structures. Typically when one applies logic to such areas as computer science, artificial intelligence or linguistics, one encounters hybrid ontologies. The aim of this paper is to identify plausible strategies for coping with ontological richness.
Reasoning about Judgment and Preference Aggregation
, 2007
"... Agents that must reach agreements with other agents need to reason about how their preferences, judgments, and beliefs might be aggregated with those of others by the social choice mechanisms that govern their interactions. The recently emerging field of judgment aggregation studies aggregation from ..."
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Cited by 5 (2 self)
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Agents that must reach agreements with other agents need to reason about how their preferences, judgments, and beliefs might be aggregated with those of others by the social choice mechanisms that govern their interactions. The recently emerging field of judgment aggregation studies aggregation from a logical perspective, and considers how multiple sets of logical formulae can be aggregated to a single consistent set. As a special case, judgment aggregation can be seen to subsume classical preference aggregation. We present a modal logic that is intended to support reasoning about judgment aggregation scenarios (and hence, as a special case, about preference aggregation): the logical language is interpreted directly in judgment aggregation rules. We present a sound and complete axiomatisation of such rules. We show that the logic can express aggregation rules such as majority voting; rule properties such as independence; and results such as the discursive paradox, Arrow’s theorem and Condorcet’s paradox – which are derivable as formal theorems of the logic. The logic is parameterised in such a way that it can be used as a general framework for comparing the logical properties of different types of aggregation – including classical preference aggregation.
Towards a logic of social welfare
 IN PROCEEDINGS OF LOFT2006
, 2006
"... We present a logic of social welfare functions. The logical language is syntactically simple, but expressive enough to express interesting and complicated properties of social welfare functions involving, e.g., quantification over both preference relations and over individual alternatives, such as ..."
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Cited by 5 (1 self)
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We present a logic of social welfare functions. The logical language is syntactically simple, but expressive enough to express interesting and complicated properties of social welfare functions involving, e.g., quantification over both preference relations and over individual alternatives, such as Arrow’s thorem.
Modal Predicates and Coequations
, 2002
"... We show how coalgebras can be presented by operations and equations. We discuss the basic properties of this presentation and compare it with the usual approach. ..."
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Cited by 5 (2 self)
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We show how coalgebras can be presented by operations and equations. We discuss the basic properties of this presentation and compare it with the usual approach.
Temporal Patterns and Modal Structure
, 1999
"... Temporal logic arose at the border of philosophy and linguistics. From the seventies onward, it became a major tool also in computer science and articial intelligence, which have turned into the most powerful source of new logical developments since. We discuss some recent themes demonstrating new c ..."
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Cited by 4 (2 self)
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Temporal logic arose at the border of philosophy and linguistics. From the seventies onward, it became a major tool also in computer science and articial intelligence, which have turned into the most powerful source of new logical developments since. We discuss some recent themes demonstrating new connections with modal logic. In the course of this, we also point out some new types of open research questions.
The Categorial FineStructure of Natural Language
, 2003
"... Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, i ..."
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Cited by 3 (1 self)
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Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, in a light examplebased manner, where this elegant logical paradigm stands when confronted with the wear and tear of reality. Starting from a brief history of the Lambek tradition since the 1980s, we discuss three main issues: (a) the fit of the lambda calculus engine to characteristic semantic structures in natural language, (b) the coexistence of the original typetheoretic and more recent modal interpretations of categorial logics, and (c) the place of categorial grammars in the complex total architecture of natural language, which involves  amongst others  mixtures of interpretation and inference.
The Mathematical MorphoLogical view on Reasoning about Space
, 2006
"... Qualitative reasoning about mereotopological relations has been extensively investigated, while more recently geometrical and spatiotemporal reasoning are gaining increasing attention. We propose to consider mathematical morphologic operators as the inspiration for a new language and inference mech ..."
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Cited by 3 (0 self)
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Qualitative reasoning about mereotopological relations has been extensively investigated, while more recently geometrical and spatiotemporal reasoning are gaining increasing attention. We propose to consider mathematical morphologic operators as the inspiration for a new language and inference mechanism to reason about space. Interestingly, the proposed morphologic captures not only traditional mereotopological relations, but also notions of relative size and morphology. The proposed representational framework is a hybrid arrow logic theory for which we define a resolution calculus which is, to the best of our knowledge, the first such calculus for arrow logics. 1