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...

Philosophical theories of logical reasoning are intrinsically related to formal models. This holds in particular of Dummett–Prawitz-style proof-theoretic semantics and calculi of natural deduction. Basic philosophical ideas of this semantic approach have a counterpart in the theory of natural deduction. For example, the “fundamental assumption” in Dummett’s theory of meaning (Dummett, 1991, p. ...

We show that soft constraints can be used to model logical reasoning, that is deduction and abduction (and induction). In particular, we focus on the abduction process and we show how it can be implemented with a (soft) constraint removal operator. As a running application example throughout the paper, we reason with access control policies and credentials. In this way, we can associate the lev...

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The short note describes the chart parser for multimodal type-logical grammars which has been developed in conjunction with the type-logical treebank for French. The chart parser presents an incomplete but fast implementation of proof search for multimodal type-logical grammars using the"deductive parsing"framework. Proofs found can be transformed to natural deduction proofs.