We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Väänänen, and their compositional semantics due to Hodges. We show how Hodges’ semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the ...

We present a complete finite axiomatization of the unrestricted implication problem for inclusion and conditional independence atoms in the context of dependence logic. For databases, our result implies a finite axiomatization of the unrestricted implication problem for inclusion, functional, and embedded multivalued dependencies in the unirelational case.

Linear logic provides a logical perspective on computational issues such as control of resources and order of evaluation. The most important feature of linear logic is that formulas are considered as actions. While classical logic treats the sentences that are always true or false, in linear logic it depends on an internal state of a dynamic system. Curry-Howard correspondence is a corresponden...

A new family of implication operators, called probabilistic implications, is introduced. The suggested implications are based on conditional copulas and make a bridge between probability theory and fuzzy logic. It is shown that some well-known fuzzy implications appear as a particular probabilistic implications. Therefore, it seems that this new family of implication operators might be a useful...

This paper presents a flexible and efficient approach to evaluating implications as well as deriving indirect implications in logic circuits. Evaluation and derivation of implications are essential in ATPG, equivalence checking, and netlist optimization. Contrary to other methods, our approach is based on a graph model of a circuit’s clause description called the implication graph. It combines ...

We provide a logical matrix semantics and Gentzen-style sequent calculus for the first-degree entailments valid in W. T. Parry’s logic of Analytic Implication. achieve former by introducing closely related to that inducing paracomplete weak Kleene logic, latter presenting where initial sequents left right rules negation are subject linguistic constraints.

As a continuation of our research work on resolutionbased automated reasoning approaches for latticevalued logic systems with truth-values in a latticevalued logical algebraic structure – lattice implication algebra (LIA), in the present paper, we prove thatα resolution for lattice-valued first-order logic ( ) LF X based on LIA can be equivalently transformed into that for lattice-valued propos...

C. I. Lewis invented modern modal logic as a theory of “strict implication” J. Over the classical propositional calculus one can as well work with the unary box connective, which became the modal primitive ever since. Over the intuitionistic propositional calculus, however, the strict implication has greater expressive power than 2 and allows to make distinctions invisible in the ordinary synta...

We present an eeective version of Ritt's algorithm. We apply material of (Boulier et al. 1995) for which we give new concise proofs. We present original results in constructive algebra that makes the algorithm exible and simple.