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A Negationless Interpretation of Intuitionistic Axiomatic Theories:
Higher-order Arithmetic
Victor N. Krivtsov
This work is a sequel to our [14] (ed: report ML-1998-06). It is shown how
Theorem 6 of [14], dealing with the translatability of {\bf HA} (Heyting's
arithmetic) into negationless arit...
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This is a bunch of papers devoted to various aspects of logical dynamics.
It is the 1998 sequel to last year's collection "Dynamic Bits and Pieces",
which appeared as ILLC Research Report LP-1997-01.
Contents
1. Exploring Logical Dynamics: The Main Lines.
2. Process Operations in Extended Dy...
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A Modal Analysis of some Principles of the Provability Logic of Heyting
Arithmetic
Rosalie Iemhoff
In this paper four principles and one scheme of the Provability Logic of
(intuitionistic) Heyting Arithmetic HA are studied from a modal-logical point
of view. These are, besides the wellknow...
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Characterization Results for dHorn Formulas
(or: On formulas that are true on Dual Reduced Products)
Carlos Areces, Ver\'onica Becher Sebasti\'an Ferro
We provide two different model theoretic characterizations of a new fragment
of firstorder logic which we call dHorn formulas. This fragme...
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In this article we establish interpolation for the minimal system of
interpretability logic IL. We prove that arrow interpolation holds for
IL and that turnstile interpolation and interpolation for the \Lambda
modality easily follow from this. Furthermore, these properties are
extended to the...
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We develop a translation-based view dual of modal logic as the study of
intensional languages that are at the same time interesting, expressive and
decidable parts of standard logical systems. This tandem approach improves
our understanding of modal logic - while at the same time, it extends t...
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Generalizing an example from Fine and inspired by a theorem in Jonsson, we
prove that any modal formula of the form \pi(p \or q) \iff \pi(p) \or \pi(q)
(with \pi(p) a positive formula) is canonical. We also prove that any such
formula is strongly sound and complete with respect to an elementar...
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With each projective geometry we can associate a Lyndon algebra.
This algebra always satisfies Tarski's axioms for relation algebras
and Lyndon algebras thus form an interesting connection between the
fields of projective geometry and algebraic logic.
In this paper we prove that if G is a clas...
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In this thesis the question raised is whether, and, if so, to what degree, we
can establish identity using linguistic means, such as names, descriptions,
indexicals and demonstratives. First, we look into different ontological
considerations; after having done that, we note that taking a stand in...
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