In Peirce Studies 1, 41— Lubbock: Institute for Studies in Pragmaticism. Nadin, Mihai Consistency, completeness and the meaning of sign theories. American Journal of Semiotics l 3 , 79— The logic of vagueness and the category of synechism. Freeman ed. Engel-Tiercelin, Claudine Vagueness and the unity of C. Transactions of the C. Peirce Society 28 1 , 51— Merrell, Floyd Semiosis in the Postmodern Age. West Lafayette: Purdue University Press.
Signs Grow: Semiosis and Life Processes. Toronto: University of Toronto Press. This by itself does not change the corresponding logic intuitionistic logic, in this case. To obtain a hypersequent calculus for the fundamental fuzzy logic MTL one has to add the communication rule to a sequent system for the contraction-free version of intuitionistic logic a well-studied example of a substructural logic.
Also labeled proof systems and various tableau calculi have been suggested. It is desirable, not only from a philosophical point of view, but also to a get a better grip on potential applications of fuzzy logics to relate the meaning of intermediary truth-values and corresponding logical connectives to basic models of reasoning with vague and imprecise notions. A number of such semantics that seek to justify particular choices of truth-functional connectives have been introduced.
Just two of them are briefly described here. Voting semantics is based on the idea that different agents voters may coherently judge the same proposition differently. Without further restrictions this does not lead to a truth-functional semantics, but rather to an assignment of probabilities to propositions. Details can be found in Lawry It consists in a game, where two players, I and you, systematically reduce logically complex assertions formulas to simpler ones according to rules like the following:.
The rules for quantified statements refer to a fixed domain, assuming that there is a constant symbol for each domain element one stipulates:. The rules for your assertions are dual. At each state of the game an occurrence of a non-atomic formula in either the multiset of current assertions by me or by you is chosen and gets replaced by subformulas, as indicated by these rules, until only atomic assertions remain.
A final game state is then evaluated according to the following betting scheme. For each atomic formula there is a corresponding experiment which may either fail or succeed, but may show dispersion, i.
A fixed failure probability, called risk value, is assigned to each experiment and thus to each atomic formula. Jeff Paris provided an overview over other semantics supporting various choices of truth-functions; in particular, re-randomizing semantics Hisdal , similarity semantics e.
Modeling reasoning with vague predicates and propositions is often cited as the main motivation for introducing fuzzy logics. There are many alternative theories of vagueness , but there is a general agreement that the susceptibility to the sorites paradox is a main feature of vagueness. Consider the following version of the paradox:. At the face of it, it seems not to be unreasonable to accept these two assumptions. By simply repeating this type of inference we arrive at the unreasonable statement.
Fuzzy logic suggests an analysis of the sorites paradox that respects the intuition that statement 2 , while arguably not totally true, is almost true. There are various ways to model this form of reasoning in t-norm based fuzzy logics that dissolve the paradox. Because fuzzy logic mimics human decision-making, it is most useful for modeling complex problems with ambiguous or distorted inputs. Due to the similarities with natural language, fuzzy logic algorithms are easier to code than standard logical programming, and require fewer instructions, thereby saving on memory storage requirements.
These advantages also come with drawbacks, due to the imprecise nature of fuzzy logic. Since the systems are designed for inaccurate data and inputs, they must be tested and validated to prevent inaccurate results. Data mining is the process of identifying significant relationships in large sets of data, a field that overlaps with statistics, machine learning, and computer science.
Fuzzy logic is a set of rules that can be used to reach logical conclusions from fuzzy sets of data. Since data mining is often applied to imprecise measurements, fuzzy logic is a useful way of determining relevant relationships from this kind of data.
Fuzzy logic is often grouped together with machine learning, but they are not the same thing. Machine learning refers to computational systems that mimic human cognition, by iteratively adapting algorithms to solve complex problems.
Fuzzy logic is a set of rules and functions that can operate on imprecise data sets, but the algorithms still need to be coded by humans. Both areas have applications in artificial intelligence and complex problem-solving.
An artificial neural network is a computational system designed to imitate the problem-solving procedures of a human-like nervous system. This is distinct from fuzzy logic, a set of rules designed to reach conclusions from imprecise data. Both have applications in computer science, but they are distinct fields. Fuzzy logic is an extension of classical logic that incorporates the uncertainties that factor into human decision-making.
It is frequently used to solve complex problems, where the parameters may be unclear or imprecise. Fuzzy logic is also used in investment software, where it can be used to interpret ambiguous or unclear trading signals.
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