22,174 research outputs found
What's Decidable About Sequences?
We present a first-order theory of sequences with integer elements,
Presburger arithmetic, and regular constraints, which can model significant
properties of data structures such as arrays and lists. We give a decision
procedure for the quantifier-free fragment, based on an encoding into the
first-order theory of concatenation; the procedure has PSPACE complexity. The
quantifier-free fragment of the theory of sequences can express properties such
as sortedness and injectivity, as well as Boolean combinations of periodic and
arithmetic facts relating the elements of the sequence and their positions
(e.g., "for all even i's, the element at position i has value i+3 or 2i"). The
resulting expressive power is orthogonal to that of the most expressive
decidable logics for arrays. Some examples demonstrate that the fragment is
also suitable to reason about sequence-manipulating programs within the
standard framework of axiomatic semantics.Comment: Fixed a few lapses in the Mergesort exampl
Externalism, internalism and logical truth
The aim of this paper is to show what sorts of logics are required by externalist and internalist accounts of the meanings of natural kind nouns. These logics give us a new perspective from which to evaluate the respective positions in the externalist--internalist debate about the meanings of such nouns. The two main claims of the paper are the following: first, that adequate logics for internalism and externalism about natural kind nouns are second-order logics; second, that an internalist second-order logic is a free logicâa second order logic free of existential commitments for natural kind nouns, while an externalist second-order logic is not free of existential commitments for natural kind nounsâit is existentially committed
On existential declarations of independence in IF Logic
We analyze the behaviour of declarations of independence between existential
quantifiers in quantifier prefixes of IF sentences; we give a syntactical
criterion for deciding whether a sentence beginning with such prefix exists
such that its truth values may be affected by removal of the declaration of
independence. We extend the result also to equilibrium semantics values for
undetermined IF sentences.
The main theorem allows us to describe the behaviour of various particular
classes of quantifier prefixes, and to prove as a remarkable corollary that all
existential IF sentences are equivalent to first-order sentences.
As a further consequence, we prove that the fragment of IF sentences with
knowledge memory has only first-order expressive power (up to truth
equivalence)
Logicism, Possibilism, and the Logic of Kantian Actualism
In this extended critical discussion of 'Kant's Modal Metaphysics' by Nicholas Stang (OUP 2016), I focus on one central issue from the first chapter of the book: Stangâs account of Kantâs doctrine that existence is not a real predicate. In §2 I outline some background. In §§3-4 I present and then elaborate on Stangâs interpretation of Kantâs view that existence is not a real predicate. For Stang, the question of whether existence is a real predicate amounts to the question: âcould there be non-actual possibilia?â (p.35). Kantâs view, according to Stang, is that there could not, and that the very notion of non-actual or âmereâ possibilia is incoherent. In §5 I take a close look at Stangâs master argument that Kantâs Leibnizian predecessors are committed to the claim that existence is a real predicate, and thus to mere possibilia. I argue that it involves substantial logical commitments that the Leibnizian could reject. I also suggest that it is danger of proving too much. In §6 I explore two closely related logical commitments that Stangâs reading implicitly imposes on Kant, namely a negative universal free logic and a quantified modal logic that invalidates the Converse Barcan Formula. I suggest that each can seem to involve Kant himself in commitment to mere possibilia
A \textsf{C++} reasoner for the description logic \shdlssx (Extended Version)
We present an ongoing implementation of a \ke\space based reasoner for a
decidable fragment of stratified elementary set theory expressing the
description logic \dlssx (shortly \shdlssx). The reasoner checks the
consistency of \shdlssx-knowledge bases (KBs) represented in set-theoretic
terms. It is implemented in \textsf{C++} and supports \shdlssx-KBs serialized
in the OWL/XML format. To the best of our knowledge, this is the first attempt
to implement a reasoner for the consistency checking of a description logic
represented via a fragment of set theory that can also classify standard OWL
ontologies.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1702.03096,
arXiv:1804.1122
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