114,655 research outputs found
Modal Logics with Hard Diamond-free Fragments
We investigate the complexity of modal satisfiability for certain
combinations of modal logics. In particular we examine four examples of
multimodal logics with dependencies and demonstrate that even if we restrict
our inputs to diamond-free formulas (in negation normal form), these logics
still have a high complexity. This result illustrates that having D as one or
more of the combined logics, as well as the interdependencies among logics can
be important sources of complexity even in the absence of diamonds and even
when at the same time in our formulas we allow only one propositional variable.
We then further investigate and characterize the complexity of the
diamond-free, 1-variable fragments of multimodal logics in a general setting.Comment: New version: improvements and corrections according to reviewers'
comments. Accepted at LFCS 201
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
First-order Goedel logics
First-order Goedel logics are a family of infinite-valued logics where the
sets of truth values V are closed subsets of [0, 1] containing both 0 and 1.
Different such sets V in general determine different Goedel logics G_V (sets of
those formulas which evaluate to 1 in every interpretation into V). It is shown
that G_V is axiomatizable iff V is finite, V is uncountable with 0 isolated in
V, or every neighborhood of 0 in V is uncountable. Complete axiomatizations for
each of these cases are given. The r.e. prenex, negation-free, and existential
fragments of all first-order Goedel logics are also characterized.Comment: 37 page
Automating Agential Reasoning: Proof-Calculi and Syntactic Decidability for STIT Logics
This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate
Systematic construction of natural deduction systems for many-valued logics
A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems
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