The standard notions of tautology and subsumption can be naturally generalized, (so that refutation completeness is preserved with respect to the associated deletion), within the context of (a speciied set of) modiied deduction rules for binary clausal resolution-refutation which build-in the reeexiv-ity, symmetry, transitivity and predicate substitutivity axioms for equality. The generalized n...

in this study, we introduce the classes of $phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. the results generalise the results of several authors in literature including xiang [chang he xiang, fixed point theorem for generalized $phi$-pseudocontra...

fuzzy logic, 67algebraic semantics, 53approximate reasoning, 6axiomatic extensions of MTL, 56 Bellman, R., 21bipolar possibilistic logic, 93BL logic, 51 canonical chain, 66canonical completeness, 66canonical extension, 83Carnap, R., 3comparative truth, 63compositionality, 29computational complexity, 73core fuzzy logic, 58 De Finetti B., 3degre...

The performance of an automated forward deduction system is crucial to its applicability. Since a forward deduction system working for discovery has no explicitly specified proposition or theorem given previously as goal, it often deduces many redundant intermediates, i.e., instances of those that have previously deduced. Therefore, how to reduce redundant intermediates is a general and difficu...

We present rst steps towards fully automated deduction that merely requires the user to submit proof problems and pick up results. Essentially, this necessitates the automation of the crucial step in the use of a deduction system, namely choosing and connguring an appropriate search-guiding heuristic. Furthermore, we motivate why learning capabilities are pivotal for satisfactory performance. T...

Equational deduction is generalised within a category-based abstract model theory framework, and proved complete under a hypothesis of quantiier projectivity, using a semantic treatment that regards quantiiers as models rather than variables, and regards valuations as model morphisms rather than functions. Applications include many and order sorted conditional] equational logics, Horn clause lo...

In this paper we discuss Gabbay’s idea of basing nonmonotonic deduction on semantic consequence in intuitionistic logic extended by a consistency operator and Turner’s suggestion of replacing the intuitionistic base system by Kleene’s three-valued logic. It is shown that a certain counterintuitive feature of these approaches can be avoided by using Nelson’s constructive logic N instead of intui...

A new predicate calculus deduction system based on production rules is proposed. The system combines several developments in Artificial Intelligence and Automatic Theorem Proving research including the use of domain-specific inference rules and separate mechanisms for forward and backward reasoning. It has a clean separation between the data base, the production rules, and the control system. G...

The rho-calculi provide enlightening concepts for both computing and reasoning as well as their combination. They consist in the generalization of lambda-calculus to structures like terms, propositions or graphs and we will show how their interrelations with deduction provide powerful frameworks for the next generation of proof assistants. 1998 ACM Subject Classification F.4.1 Mathematical Logi...

In this paper, we considered the half logistic model and derived a probability density function that generalized it. The cumulative distribution function, the $n^{th}$ moment, the median, the mode and the 100$k$-percentage points of the generalized distribution were established. Estimation of the parameters of the distribution through maximum likelihood method was accomplished with the aid of c...