64,032 research outputs found
A Cut-Free Sequent Calculus for Defeasible Erotetic Inferences
In recent years, the effort to formalize erotetic inferences (i.e., inferences
to and from questions) has become a central concern for those working
in erotetic logic. However, few have sought to formulate a proof theory
for these inferences. To fill this lacuna, we construct a calculus for (classes
of) sequents that are sound and complete for two species of erotetic inferences
studied by Inferential Erotetic Logic (IEL): erotetic evocation and regular erotetic implication. While an attempt has been made to axiomatize the former in a sequent
system, there is currently no proof theory for the latter. Moreover, the extant
axiomatization of erotetic evocation fails to capture its defeasible character
and provides no rules for introducing or eliminating question-forming operators.
In contrast, our calculus encodes defeasibility conditions on sequents and
provides rules governing the introduction and elimination of erotetic formulas.
We demonstrate that an elimination theorem holds for a version of the cut
rule that applies to both declarative and erotetic formulas and that the rules
for the axiomatic account of question evocation in IEL are admissible in our
system
Labelled sequent calculi for logics of strict implication
n this paper we study the proof theory of C.I. Lewis’ logics of strict conditional S1-
S5 and we propose the first modular and uniform presentation of C.I. Lewis’ systems.
In particular, for each logic Sn we present a labelled sequent calculus G3Sn and we
discuss its structural properties: every rule is height-preserving invertible and the
structural rules of weakening, contraction and cut are admissible. Completeness of
G3Sn is established both indirectly via the embedding in the axiomatic system Sn
and directly via the extraction of a countermodel out of a failed proof search. Finally,
the sequent calculus G3S1 is employed to obtain a syntactic proof of decidability of
S1
Cut-Simulation and Impredicativity
We investigate cut-elimination and cut-simulation in impredicative
(higher-order) logics. We illustrate that adding simple axioms such as Leibniz
equations to a calculus for an impredicative logic -- in our case a sequent
calculus for classical type theory -- is like adding cut. The phenomenon
equally applies to prominent axioms like Boolean- and functional
extensionality, induction, choice, and description. This calls for the
development of calculi where these principles are built-in instead of being
treated axiomatically.Comment: 21 page
Structural completeness in propositional logics of dependence
In this paper we prove that three of the main propositional logics of
dependence (including propositional dependence logic and inquisitive logic),
none of which is structural, are structurally complete with respect to a class
of substitutions under which the logics are closed. We obtain an analogues
result with respect to stable substitutions, for the negative variants of some
well-known intermediate logics, which are intermediate theories that are
closely related to inquisitive logic
Iterated reflection principles over full disquotational truth
Iterated reflection principles have been employed extensively to unfold
epistemic commitments that are incurred by accepting a mathematical theory.
Recently this has been applied to theories of truth. The idea is to start with
a collection of Tarski-biconditionals and arrive by finitely iterated
reflection at strong compositional truth theories. In the context of classical
logic it is incoherent to adopt an initial truth theory in which A and 'A is
true' are inter-derivable. In this article we show how in the context of a
weaker logic, which we call Basic De Morgan Logic, we can coherently start with
such a fully disquotational truth theory and arrive at a strong compositional
truth theory by applying a natural uniform reflection principle a finite number
of times
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