and introduction. The condensed detachment rule, or rule D, was first proposed by Carew Meredith in the 1950's for propositional logic based on implication. It is a combination of modus ponens with a "minimal" amount of substitution. We shall give a precise detailed statement of rule D. (Some attempts in the published literature to do this have been inaccurate.) The D-completeness question for ...

In this paper we consider propositional calculi, which are finitely axiomatizable extensions of intuitionistic implicational propositional calculus together with the rules of modus ponens and substitution. We give a proof of undecidability of the following problem for these calculi: whether a given finite set of propositional formulas constitutes an adequate axiom system for a fixed proposition...

We contribute to the theory of implications and conjunctions related by adjointness, in multiple-valued logics. We suggest their use in Zadeh s compositional rule of inference, to interpret generalized modus ponens inference schemata. We provide new complete characterizations of implications that distinguish left arguments, implications that satisfy the exchange principle, divisible conjunction...

In this paper I defend the tenability of the Thesis that the probability of a conditional equals the conditional probability of the consequent given the antecedent. This is done by adopting the view that the interpretation of a conditional may differ from context to context. Several triviality results are (re-)evaluated in this view as providing natural constraints on probabilities for conditio...

Some intuitive normative principles raise vexing ‘detaching problems’ by their failure to license modus ponens. I examine three such principles (a self-reliance principle and two different instrumental principles) and recent stategies employed to resolve their detaching problems. I show that solving these problems necessitates postulating an indefinitely large number of senses for ‘ought’. The ...

Nowadays, people start to accept fuzzy rule–based systems as flexible and convenient tools to solve a myriad of ill–defined but otherwise (for humans) straightforward tasks such as controlling fluid levels in a reactor, automatical lens focussing in cameras and adjusting an aircraft’s navigation to the change of winds and so on. Contrary to the intuition often seen as the feeding ground of fuzz...

Inconsistency handling in expressive description logics is an important problem because inconsistency may naturally occur in an open world. In this paper, we first present the quasi-classical semantics for description logic SHIQ, which is based on quasi-classical logic. We show that this semantics can be used to deal with inconsistency and that it is reduced to the standard semantics when there...

We define the notion of the uniform reduct of a propositional proof system as the set of those bounded formulas in the language of Peano Arithmetic which have polynomial size proofs under the Paris-Wilkietranslation. With respect to the arithmetic complexity of uniform reducts, we show that uniform reducts are Π1-hard and obviously in Σ2. We also show under certain regularity conditions that ea...

Resumen Tomando como base las ideas presentadas en [1], general-izamos algunos de sus resultados a programas disyuntivos; dichas gen-eralizaciones se obtendrán extendiendo el siguiente resultado presentado en [1]: Dado un programa normal P y a unátomo, se tiene que P C a si, y sólo si, P C ω a. Junto con la regla de inferencia Modus Ponens (MP) que nos permite obtener ψ de ϕ y ϕ → ψ. Esta regla...