We give a complete characterization of Priest's Finite Inconsistent Arithmetics observing that his original putative characterization included arithmetics which cannot in fact be realized. 相似文献
A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell’s Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob’s assumption is wrongThis is formalized to show that any belief model of a certain kind must have a ‘hole.’ An interpretation of the result is that if the analyst’s tools are available to the players in a game, then there are statements that the players can think about but cannot assume. Connections are made to some questions in the foundations of game theory.Special Issue Ways of Worlds II. On Possible Worlds and Related Notions Edited by Vincent F. Hendricks and Stig Andur Pedersen 相似文献
We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates.
After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV
algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers.
Presented by Heinrich Wansing相似文献
A proposal by Ferguson [2003, Argumentation17, 335–346] for a fully monotonic argument form allowing for the expression of defeasible generalizations is critically examined and rejected as a general solution. It is argued that (i) his proposal reaches less than the default-logician’s solution allows, e.g., the monotonously derived conclusion is one-sided and itself not defeasible. (ii) when applied to a suitable example, his proposal derives the wrong conclusion. Unsuccessful remedies are discussed. 相似文献
This paper presents Automath encodings (which are also valid in LF/λP) of various kinds of foundations of mathematics. Then it compares these encodings according to their size, to find out which foundation is the simplest.
The systems analyzed in this way are two kinds of set theory (ZFC and NF), two systems based on Church's higher order logic (Isabelle/Pure and HOL), three kinds of type theory (the calculus of constructions, Luo's extended calculus of constructions, and Martin-Löf's predicative type theory) and one foundation based on category theory.
The conclusions of this paper are that the simplest system is type theory (the calculus of constructions), but that type theories that know about serious mathematics are not simple at all. In that case the set theories are the simplest. If one looks at the number of concepts needed to explain such a system, then higher order logic is the simplest, with twenty-five concepts. On the other side of the scale, category theory is relatively complex, as is Martin-Löf's type theory.
(The full Automath sources of the contexts described in this paper are one the web at http://www.cs.ru.nl/~freek/zfc-etc/.) 相似文献
This paper makes a point about the interpretation of the simplestquantified modal logic, that is, quantified modal logic witha single domain. It is commonly assumed that the domain in questionis to be understood as the set of all possibile objects. Thepoint of the paper is that this assumption is misguided. 相似文献
We investigate certain aspects of the first-order theory oforthogonality structures - structures consisting of a domainof lines subject to a binary orthogonality relation. In particular,we establish definitions of various geometric and algebraicnotions in terms of orthogonality, describe the constructionof extremal subspaces using orthogonality, and show that thefirst-order theory of line orthogonality in the Euclidean n-spaceis not 0-categorical for n 3. 相似文献
Within the program of finding axiomatizations for various parts of computability logic, it was proven earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting’s intuitionistic
calculus. That sort of reduction permits unlimited reusage of the computational resource represented by the antecedent. An
at least equally basic and natural sort of algorithmic reduction, however, is the one that does not allow such reusage. The
present article shows that turning the logic of the first sort of reduction into the logic of the second sort of reduction
takes nothing more than just deleting the contraction rule from its Gentzen-style axiomatization. The first (Turing) sort
of interactive reduction is also shown to come in three natural versions. While those three versions are very different from
each other, their logical behaviors (in isolation) turn out to be indistinguishable, with that common behavior being precisely
captured by implicative intuitionistic logic. Among the other contributions of the present article is an informal introduction
of a series of new — finite and bounded — versions of recurrence operations and the associated reduction operations.
Presented by Robert Goldblatt 相似文献
The paper presents predicate logical extensions of some subintuitionistic logics. Subintuitionistic logics result if conditions
of the accessibility relation in Kripke models for intuitionistic logic are dropped. The accessibility relation which interprets
implication in models for the propositional base subintuitionistic logic considered here is neither persistent on atoms, nor
reflexive, nor transitive. Strongly complete predicate logical extensions are modeled with a second accessibility relation,
which is a partial order, for the interpretation of the universal quantifier.
Presented by Melvin Fitting 相似文献
If the language is extended by new individual variables, in classical first order logic, then the deduction system obtained
is a conservative extension of the original one. This fails to be true for the logics with infinitary predicates. But it is
shown that restricting the commutativity of quantifiers and the equality axioms in the extended system and supposing the merry-go-round
property in the original system, the foregoing extension is already conservative. It is shown that these restrictions are
crucial for an extension to be conservative. The origin of the results is algebraic logic.
Presented by Daniele Mundici
Supported by grant OTKA T43242. 相似文献