It is shown the complete equivalence between the theory of continuous (enumeration) fuzzy closure operators and the theory of (effective) fuzzy deduction systems in Hilbert style. Moreover, it is proven that any truth-functional semantics whose connectives are interpreted in [0,1] by continuous functions is axiomatizable by a fuzzy deduction system (but not by an effective fuzzy deduction syste...

The combinatorics of proof-search in classical propositional logic lies at the heart of most eecient proof procedures because the logic admits least-commitment search. The key to extending such methods to quantiiers and non-classical connectives is the problem of recovering this least-commitment principle in the context of the non-classical/non-propositional logic; i.e., characterizing when a l...

Using logics to express program properties, and deduction systems for proving properties of programs, gives a very elegant way of deening program analysis techniques. This paper addresses a shortcoming of previous work in the area by establishing a more general framework for such logics, as is commonly done for progam analysis using abstract interpretation. Moreover, there are natural extension...

Writing is "good" when it anticipates the knowledge that its readers will bring to it-the questions they will implicitly ask-and tailors its content and form accordingly. A large part of this tailoring involves the careful use of "discourse clues": choices of wording, patterns of phrasing, and specific discourse connectives that signal the structure and intent of a text to the audience. We begi...

Bill Stiles wants to enhance the reliability and the utility of theory-building case studies. To do so, he proposes a systematic, replicable approach to clinical case materials that to date has been difficult to use systematically. At the core of his proposal is what he calls “logical operations,” which include some familiar elements of logic: deduction, induction, and abduction. While not with...

Gentzen’s and Prawitz’s approach to deductive systems, and Carnap’s and Popper’s treatment of probability in logic were two fruitful ideas of logic in the mid-twentieth century. By combining these two concepts, the notion of sentence probability, and the deduction relation formalized by means of inference rules, we introduce a system of inference rules based on the traditional proof-theoretic p...

We consider proofs in minimal logic, written in natural deduction style. The only rules are introduction and elimination for implication and the universal quantifier. The logical connectives ∃,∧ are seen as special cases of inductively defined predicates, and hence are defined by the introduction and elimination schemes ∀x(A→ ∃xA), ∃xA→ ∀x(A→ B)→ B (x not free in B), A→ B → A ∧B, A ∧B → (A→ B →...

Polymorphism has become a common way of designing short and reusable programs by abstracting generic definitions from typespecific ones. Such a convenience is valuable in logic as well, because it unburdens the specifier from writing redundant declarations of logical symbols. However, top shelf automated theorem provers such as Simplify, Yices or other SMT-LIB ones do not handle polymorphism. T...

universit a di genova facolt a di ingegneria dipartimento informatica sistemistica telematica Abstract The goal of this paper is to present a reasoning system, called METAFOL, embodying the features of a self-reeective system, i.e. a system which has a representation of its own code and is able to reason about and, possibly, extend or modify it. These features have been achieved by employing a ...

. The reason for including this chapter is to make the book as selfcontained as possible. It should in particular be accessible to physicists, who normally have no training in formal logic. We present the basics of classical propositional logic and non-monotonic logic. In fact, it is possible to provide the reader with all the logical equipment he needs in order to understand the logical invest...