1,883 research outputs found
Merging fragments of classical logic
We investigate the possibility of extending the non-functionally complete
logic of a collection of Boolean connectives by the addition of further Boolean
connectives that make the resulting set of connectives functionally complete.
More precisely, we will be interested in checking whether an axiomatization for
Classical Propositional Logic may be produced by merging Hilbert-style calculi
for two disjoint incomplete fragments of it. We will prove that the answer to
that problem is a negative one, unless one of the components includes only
top-like connectives.Comment: submitted to FroCoS 201
Sequent Calculi for the classical fragment of Bochvar and Halld\'en's Nonsense Logics
In this paper sequent calculi for the classical fragment (that is, the
conjunction-disjunction-implication-negation fragment) of the nonsense logics
B3, introduced by Bochvar, and H3, introduced by Halld\'en, are presented.
These calculi are obtained by restricting in an appropriate way the application
of the rules of a sequent calculus for classical propositional logic CPL. The
nice symmetry between the provisos in the rules reveal the semantical
relationship between these logics. The Soundness and Completeness theorems for
both calculi are obtained, as well as the respective Cut elimination theorems.Comment: In Proceedings LSFA 2012, arXiv:1303.713
Incompleteness of a first-order Gödel logic and some temporal logics of programs
It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal logic of linear discrete time with gaps follows
- …