Definite descriptions are widely discussed in linguistics and formal semantics, but their formal treatment in logic is surprisingly modest. In this article we present a sound, complete, and cut-free tableau calculus T...
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Definite descriptions are widely discussed in linguistics and formal semantics, but their formal treatment in logic is surprisingly modest. In this article we present a sound, complete, and cut-free tableau calculus TCR lambda for the logic L-R lambda being a formalisation of a Russell-style theory of definite descriptions with the iota-operator used to construct definite descriptions, the lambda-operator forming predicate-abstracts, and definite descriptions as genuine terms with a restricted right of residence. We show that in this setting we are able to overcome problems typical of Russell's original theory, such as scoping difficulties or undesired inconsistencies. We prove the Craig interpolation property for the proposed theory, which, through the Beth definability property, allows us to check whether an individual constant from a signature has a definite description-counterpart under a given theory.
In standard epistemic logic, the names and the existence of agents are usually assumed to be common knowledge implicitly. This is unreasonable for various applications in computer science and philosophy. Inspired by t...
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In standard epistemic logic, the names and the existence of agents are usually assumed to be common knowledge implicitly. This is unreasonable for various applications in computer science and philosophy. Inspired by term-modal logic and assignment operators in dynamic logic, we introduce a lightweight modal predicate logic where names can be non-rigid, and the existence of agents can be uncertain. The language can handle various de dicto/de re distinctions in a natural way. We characterize the expressive power of our language, obtain complete axiomatisations of the logics over several classes of varying-domain/constant-domain epistemic models, and show their (un)decidability. (C) 2021 Elsevier B.V. All rights reserved.
A paradox about sets of properties is presented. The paradox, which invokes an impredicatively defined property, is formalized in a free third-order logic with lambda-abstraction, through a classically proof-theoretic...
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A paradox about sets of properties is presented. The paradox, which invokes an impredicatively defined property, is formalized in a free third-order logic with lambda-abstraction, through a classically proof-theoretically valid deduction of a contradiction from a single premise to the effect that every property has a unit set. Something like a model is offered to establish that the premise is, although classically inconsistent, nevertheless consistent, so that the paradox discredits the logic employed. A resolution through the ramified theory of types is considered. Finally, a general scheme that generates a family of analogous paradoxes and a generally applicable resolution are proposed.
Czech indefinite pronouns like nekdo 'someone' (unlike indefinite nouns like penize 'money') cannot be pronounced in their base (postverbal) position unless they are interpreted as narrowly focused. Br...
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Czech indefinite pronouns like nekdo 'someone' (unlike indefinite nouns like penize 'money') cannot be pronounced in their base (postverbal) position unless they are interpreted as narrowly focused. Broad focus (focus on the whole verb phrase) is only facilitated with indefinite pronouns in a derived (preverbal) position. The analysis in this paper makes use of the fact that Czech indefinite pronouns are morphologically related to wh-words. It is argued that wh-words in Czech denote lambda-operators, which are viewed as functions from truth values to predicates. It follows that wh-words (and indefinite pronouns) must be interpreted in the sister-node of an expression denoting a truth value and therefore can never be interpreted in their base position. Finally, it is suggested how the analysis could be used to account for the behavior of the indefinite pronoun kdokoliv 'anyone', which is (under certain conditions) interpreted as a free choice item in a narrow focus (postverbal) position and as a negative polarity item in a broad focus (preverbal) position.
Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. In contrast, Whitehead and Russel...
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Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. In contrast, Whitehead and Russell reduced an important part of mathematics to logic by defining functions in terms of relations (using the definite description operator). We argue that there is a reason to prefer Whitehead and Russell's reduction of functions to relations over Frege's reduction of relations to functions. There is an interesting system having a logic that can be properly characterized in relational type theory (RTT) but not in functional type theory (FTT). This shows that RTT is more general than FTT. The simplification offered by Church in his FTT is an over-simplification: one cannot assimilate predication to functional application.
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