# Fuzzy logic, continuity and effectiveness

@article{Biacino2002FuzzyLC, title={Fuzzy logic, continuity and effectiveness}, author={Loredana Biacino and Giangiacomo Gerla}, journal={Archive for Mathematical Logic}, year={2002}, volume={41}, pages={643-667} }

Abstract. 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 system, in general).

## 75 Citations

### Effectiveness and multivalued logics

- Computer ScienceJournal of Symbolic Logic
- 2006

Effective domain theory is applied to fuzzy logic to give suitable notions of semi-decidable and decidable L-subset and to investigate about the effectiveness of the fuzzy deduction apparatus.

### Church Thesis for fuzzy logic

- Computer Science
- 2007

Effective domain theory is applied to fuzzy logic to give suitable notions of semi-decidable and decidable L-subset and shows the inadequateness of these definitions and the difficulties in formulating an analogue of Church Thesis for fuzzy logic.

### Chapter 15 FUZZY REASONING

- Computer Science
- 2007

Fuzzy Reasoning is based on the theory of fuzzy sets and it encompasses Artificial IntelHgence, information processing and theories from logic to pure and applied mathematics, like graph theory,…

### Multi-valued Logics, Effectiveness and Domains

- Computer ScienceCiE
- 2007

Effective domain theory is applied to fuzzy logic to give suitable notions of semi-decidable and decidable L-subset and shows the inadequateness of these definitions and the difficulties in formulating an analogue of Church Thesis for fuzzy logic.

### Comments on some theories of fuzzy computation

- Computer ScienceInt. J. Gen. Syst.
- 2016

The basic idea of this paper is that the presence of real numbers in the interval [0,1] forces us to refer to endless approximation processes ( as in recursive analysis) and not to processes terminating after a finite number of steps and giving the exact output (as in recursive arithmetic).

### Automata theory based on complete residuated lattice-valued logic

- Mathematics, Computer ScienceScience in China Series : Information Sciences
- 2007

A fundamental framework of automata theory based on complete residuated lattice-valued logic is established and its basic properties are discussed, from which it follows that the two fuzzy operators are exactly fuzzy closure operators.

### Closure properties for fuzzy recursively enumerable languages and fuzzy recursive languages

- Computer ScienceJ. Intell. Fuzzy Syst.
- 2016

The concept of non-deterministic fuzzy Turing machine - NTFM is generalized, replacing the t-norm operator for several aggregation functions and establishing the languages accepted by these machines, called fuzzy recursively enumerable languages or simply LFRE and which classes of LFRE are closed under unions and intersections.

### Giangiacomo Gerla VAGUENESS AND FORMAL FUZZY LOGIC : Some criticisms

- Philosophy
- 2017

In the common man reasoning the presence of vague predicates is pervasive and under the name “fuzzy logic in narrow sense” or “formal fuzzy logic” there are a series of attempts to formalize such a…

### The Continuous Logic

- Philosophy, Computer Science
- 2015

This paper presents the continuous logic with the truth value of a proposition falls into the con-tinuous range [0,1], where 0 stands for complete falsity and 1 for complete truth.

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