1,132 research outputs found
Minimal Negation in the Ternary Relational Semantics
Minimal Negation is defined within the basic positive relevance logic in the relational ternary semantics: B+. Thus, by defining a number of subminimal negations in the B+ context, principles of weak negation are shown to be isolable. Complete ternary semantics are offered for minimal negation in B+. Certain forms of reductio are conjectured to be undefinable (in ternary frames) without extending the positive logic. Complete semantics for such kinds of reductio in a properly extended positive logic are offered
Converse Ackermann Property and Minimal Negation
A logic S has the Converse Ackermann Property (CAP) if non-necessitive propositions are not derivable in S from necessitive ones. We show in this paper how to introduce minimal negation in positive logics with the CAP. Relational ternary semantics are provided for all the logics considered in this paper
Extensions of the basic constructive logic for weak consistency BKc1 defined with a falsity constant
The logic BKc1 is the basic constructive logic for weak consistency (i.e., absence of the negation of a theorem) in the ternary relational semantics without a set of designated points. In this paper, a number of extensions of B Kc1 defined with a propositional falsity constant are defined. It is also proved that weak consistency is not equivalent to negation-consistency or absolute consistency (i.e., non-triviality) in any logic included in positive contractionless intermediate logic LC plus the constructive negation of BKc1 and the (constructive) contraposition axioms
A Variety of DeMorgan Negations in Relevant Logics
The present paper is inspired by Sylvan and Plumwoodâs logicBM defined in âNon-normal relevant logicsâ and by their treatmentof negation with the â-operator in âThe semantics of first-degree en-tailmentâ. Given a positive logic L including Routley and Meyerâsbasic positive logic and included in either the positive fragment of Eor in that of RW, we investigate the essential De Morgan negation ex-pansions of L and determine all the deductive relations they maintainto each other. A Routley-Meyer semantics is provided for each logicdefined in the paper
Converse Ackermann property and constructive negation defined with a negation connective
The Converse Ackermann Property is the unprovability of formulas of the form (A -> B) -> C when C does contain neither -> nor ÂŹ. Intuitively, the CAP amounts to rule out the derivability of pure non-necessitive propositions from non-necessitive ones. A constructive negation of the sort historically defined by, e.g., Johansson is added to positive logics with the CAP in the spectrum delimited by Ticket Entailment and Dummettâs logic LC
Answer Sets for Consistent Query Answering in Inconsistent Databases
A relational database is inconsistent if it does not satisfy a given set of
integrity constraints. Nevertheless, it is likely that most of the data in it
is consistent with the constraints. In this paper we apply logic programming
based on answer sets to the problem of retrieving consistent information from a
possibly inconsistent database. Since consistent information persists from the
original database to every of its minimal repairs, the approach is based on a
specification of database repairs using disjunctive logic programs with
exceptions, whose answer set semantics can be represented and computed by
systems that implement stable model semantics. These programs allow us to
declare persistence by defaults and repairing changes by exceptions. We
concentrate mainly on logic programs for binary integrity constraints, among
which we find most of the integrity constraints found in practice.Comment: 34 page
- âŠ