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This is a chapter in the forthcoming "Handbook of Modal Logic",
written as an introduction to the modus operandi of keeping a balance
between expressive power and complexity found in modal languages. With
this theme as a running thread, we survey the basic model theory of
modal logic over both mo...
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In this paper we take up the study of Henkin quantifiers with boolean
variables also known as partially ordered connectives. We consider
first-order formulae prefixed by partially ordered connectives,
denoted D, on finite structures. We characterize D as a fragment of
second-order existential log...
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In this paper, we study the game-theoretic and computational repercussions
of Henkins partially ordered quantifiers. After defining a gametheoretic
semantics for these objects, we observe that tuning the parameter
of absentmindedness gives rise to quantifier prefixes studied. In the
interest of c...
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Both logic and game theory have developed an interest in analyzing
what constitutes rational behaviour under uncertainty. One particular
interesting encounter between logic and game theory is the use of
belief revision techniques as a means of analysis of games.
The game-theoretic analysis of ra...
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This paper explores ways to introduce commitment, as conceived in
terms of plans and intentions, into decision theory. An
intention-based representation theorem is proved, along with a
proposal to model how plans simplify decision making for
resource-bounded agents.
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We discuss the thesis formulated by Hintikka (1973) that certain
natural language sentences require non-linear quantification to
express their meaning. Our basic assumption is that a criterion for
adequacy of meaning representation is compatibility with sentence
truth-conditions. This can be est...
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We discuss the neuroimaging study (McMillan et al., 2005). According
to the authors their results verify a particular computational model
of natural language quantifier comprehension posited by several
linguists and logicians (see Van Benthem, 1986). We challenge this
statement by evoking the com...
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Diversity of agents is investigated in the context of standard
epistemic logic, dynamic information update, and belief revision. We
provide a systematic discussion of different sources of diversities,
such as introspection ability, powers of observation, memory capacity,
and revision policies. In...
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We define preference in terms of a constraint sequence, a concept from
optimality theory. In case agents only have incomplete information,
beliefs are introduced. We propose three definitions to describe
dierent procedures agents may follow to get a preference relation
using the incomplete inform...
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The motivation behind this paper is to look at temporal information in
models of BMS product update. That is, it may be useful to look at
models produced through taking products with action models, as being
structurally similar to game trees. So a state in a product can be
seen as encoding a hist...
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We consider the notion of "everyday language". We claim that everyday
language is semantically bounded by properties expressible in the
existential fragment of second-order logic. Two arguments for this
thesis are formulated. Firstly, we show that so-called Barwise's test
of negation normality (B...