We present and discuss various formalizations of Modal Logics in Logical Frameworks based on Type Theories. We consider both Hilbertand Natural Deduction-style proof systems for representing both truth (local) and validity (global) consequence relations for various Modal Logics. We introduce several techniques for encoding the structural peculiarities of necessitation rules, in the typed λ-calc...

We present a method for defining logical frameworks as a collection of features which are defined and behave independently of one another. Each feature is a set of grammar clauses and rules of deduction such that the result of adding the feature to a framework is a conservative extension of the framework itself. We show how several existing logical frameworks can be so built, and how several mu...

This paper proposes and investigates an approach to deduction in probabilistic logic, using as its medium a language that generalizes the propositional version of Nilsson's probabilistic logic by incorporating conditional probabilities. Unlike many other approaches to deduction in probabilistic logic, this approach is based on inference rules and therefore can produce proofs to explain how conc...

Linear logic (LL) [9], [10](see Appendix A, B) is the logical foundation of some typetheoretic languages and also of environments for specification and theorem proving. In this paper, we consider the Multiplicative fragment of Linear Logic (MLL) from an automated deduction point of view. We propose an automated deduction (Automatic Proof Nets Construction and its implementation) based on the no...

This paper presents an approach to approximate reasoning over a set of IF-THEN rules called fuzzy logic deduction. It understands IF-THEN rules as linguistically expressed logical implications and interprets them inside formal logical theory. Methodology and some properties

This paper presents the foundations for using automated deduction technology in static program analysis. The central principle is the use of logical lattices – a class of lattices defined on logical formulas in a logical theory – in an abstract interpretation framework. Abstract interpretation over logical lattices, called logical interpretation, raises new challenges for theorem proving. We pr...

A Introduction Computation in a number of uncertainty formalisms has recently been revolutionized by the notion of local computation. 9] and 6] showed how Bayesian probability could be eeciently propagated in a network of variables; this has already lead to sizeable successful applications, as well as a large body of literature on these Bayesian networks and related issues (e.g., the majority o...

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...