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... We say that cp is valid in M, and write M i= cp, if (M, w ) i= cp for all respect to 9). w E W,. We then define (T FA cp to hold if M .[a] implies M t= ~ [ c p ] for all M E A and all substitutions 7. For example, defining truth in modal logic with respect to pairs ( M ,w) consisting of a Kripke str ...
Ground Nonmonotonic Modal Logics - Dipartimento di Informatica e
Ground Nonmonotonic Modal Logics - Dipartimento di Informatica e

... Recently, there have been a number of attempts to reconcile fix-point and semantic characterizations of modal nonmonotonic logics. In particular, Schwarz [30] proposed a semantics for McDermott and Doyle’s logics. However, the notion of minimal knowledge underlying the above cited works is stronger ...
Everything Else Being Equal: A Modal Logic for Ceteris Paribus
Everything Else Being Equal: A Modal Logic for Ceteris Paribus

... a reflexive and transitive accessibility relation  over states, interpreted as a betterness relation, with the accessible states those that are at least as good as the present one. To reason about strict preferences, we take the strict subrelation of  given by u  v & v  u, and we write this as u ...
Relevant Logic A Philosophical Examination of Inference Stephen Read February 21, 2012
Relevant Logic A Philosophical Examination of Inference Stephen Read February 21, 2012

thèse - IRIT
thèse - IRIT

... In the beginning of the 90s, Gelfond has introduced epistemic specifications (E-S) as an extension of disjunctive logic programming by epistemic notions. The underlying idea of E-S is to correctly reason about incomplete information, especially in situations when there are multiple answer sets. Rela ...
AN EXPOSITION ANS DEVELOPMENT OF KANGER`S EARLY
AN EXPOSITION ANS DEVELOPMENT OF KANGER`S EARLY

Adequate set of connectives
Adequate set of connectives

Programming in Logic Without Logic Programming
Programming in Logic Without Logic Programming

... isa(book, item), do not include time parameters. Temporal constraint predicates, including inequalities of the form T1 < T2 and T1  T2 between timepoints, and functional relationships among timepoints, such as max(T1, T2, T) and min(T1, T2, T) have only time parameters. In KELPS, temporal constrain ...
The Foundations
The Foundations

The Foundations
The Foundations

A Logical Expression of Reasoning
A Logical Expression of Reasoning

... reasoning, or even “rationality”, has been taken as synonymous. However, real life reasoning, meaning a wide range of forms of inference, covering from common sense to scientific reasoning, passing through reasoning required for technical professional practice, such as in law, economics, medicine an ...
The Foundations
The Foundations

...  A language(Vocabulary) for expressing them.  A concise notation(Syntax) for writing them.  A methodology for objectively reasoning about their truth or falsity (Semantics and Axiomatics).  It is the foundation for expressing formal proofs in all branches of mathematics. ...
MATHEMATICAL LOGIC FOR APPLICATIONS
MATHEMATICAL LOGIC FOR APPLICATIONS

... certain aspects of reasoning needed in everyday practice. Philosopher, mathematician and engineers all use the same logical techniques, i.e., formal languages, structures, proof systems, classical and non-classical logics, the difference between their approaches residing in where exactly they put th ...
relevance logic - Consequently.org
relevance logic - Consequently.org

... co-workers, and shall mention other approaches only insofar as they bear on this program. By way of minor recompense we mention that Anderson and Belnap [1975] have been good about discussing related approaches, especially the older ones. Finally, we should say that our paradigm of a relevance logic ...
The Foundations
The Foundations

...  A language(Vocabulary) for expressing them.  A concise notation(Syntax) for writing them.  A methodology for objectively reasoning about their truth or falsity (Semantics and Axiomatics).  It is the foundation for expressing formal proofs in all branches of mathematics. ...
Reading 2 - UConn Logic Group
Reading 2 - UConn Logic Group

Practical Reasoning: An Opinionated Survey.
Practical Reasoning: An Opinionated Survey.

... (“hot”), there is reasoning between the initial emotional storm and the action. Example 15. Conversation. Conversation provides many good examples of deliberative reasoning. Where there is conscious deliberation, it is likely to be devoted to content selection. But the reasoning that goes into decid ...
preliminary version
preliminary version

The Foundations
The Foundations

...  A language(Vocabulary) for expressing them.  A concise notation(Syntax) for writing them.  A methodology for objectively reasoning about their truth or falsity (Semantics and Axiomatics).  It is the foundation for expressing formal proofs in all branches of mathematics. ...
Belief Base Change Operations for Answer Set Programming
Belief Base Change Operations for Answer Set Programming

Classical Propositional Logic
Classical Propositional Logic

... A model, interpretation, or assignment v is a function from propositional parameters to truth values—in classical logic, {0, 1}, where 0 represents falsehood and 1 represents truth. ...
Combining Paraconsistent Logic with Argumentation
Combining Paraconsistent Logic with Argumentation

... Caminada, Carnielli and Dunne [5] formulated a new set of rationality postulates in addition to those of Caminada and Amgoud [3], to characterise cases under which the trivialisation problem is avoided (called the postulates of non-interference and crashresistance). The problem can then be reformula ...
The Development of Mathematical Logic from Russell to Tarski
The Development of Mathematical Logic from Russell to Tarski

Combinations of Case-Based Reasoning with Other Intelligent Methods (short paper)
Combinations of Case-Based Reasoning with Other Intelligent Methods (short paper)

In order to define the notion of proof rigorously, we would have to
In order to define the notion of proof rigorously, we would have to

... quite nicely the “natural” rules of reasoning that one uses when proving mathematical statements. This does not mean that it is easy to find proofs in such a system or that this system is indeed very intuitive! ...
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Fuzzy logic



Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1. By contrast, in Boolean logic, the truth values of variables may only be 0 or 1. Fuzzy logic has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false. Furthermore, when linguistic variables are used, these degrees may be managed by specific functions.The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by Lotfi A. Zadeh. Fuzzy logic has been applied to many fields, from control theory to artificial intelligence. Fuzzy logic had however been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski.
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