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Axiomatization of a Basic Logic of Logical Bilattices
A sequential axiomatization is given for the 16-valued logic that has been proposed by Shramko-Wansing (J Philos Logic 34:121–153, 2005) as a candidate for the basic logic of logical bilattices
Wittgenstein's Programme of a New Logic
The young Wittgenstein called his conception of logic “New Logic” and opposed it to
the “Old Logic”, i.e. Frege’s and Russell’s systems of logic. In this paper the basic
objects of Wittgenstein’s conception of a New Logic are outlined in contrast to
classical logic. The detailed elaboration of Wittgenstein’s conception depends on the
realization of his ab-notation for first order logic
Compactness of first-order fuzzy logics
One of the nice properties of the first-order logic is the compactness of
satisfiability. It state that a finitely satisfiable theory is satisfiable.
However, different degrees of satisfiability in many-valued logics, poses
various kind of the compactness in these logics. One of this issues is the
compactness of -satisfiability. Here, after an overview on the results
around the compactness of satisfiability and compactness of -satisfiability
in many-valued logic based on continuous t-norms (basic logic), we extend the
results around this topic. To this end, we consider a reverse semantical
meaning for basic logic. Then we introduce a topology on and
that the interpretation of all logical connectives are continuous with respect
to these topologies. Finally using this fact we extend the results around the
compactness of satisfiability in basic ogic
Revising Z: part II - logical development
This is the second of two related papers. In "Revising Z: Part I - logic and semantics" (this journal) we introduced a simple specification logic ZC comprising a logic and a semantics (in ZF set theory). We then provided an interpretation for (a rational reconstruction of) the specification language Z within ZC. As a result we obtained a sound logic for Z, including the basic schema calculus. In this paper we extend the basic framework with more sophisticated features (including schema operations) and we mount a critique of a number of concepts used in Z. We further demonstrate that the complications and confusions which these concepts introduce can be avoided without compromising expressibility
Revising Z: part I - logic and semantics
This is the first of two related papers. We introduce a simple specification logic ZC comprising a logic and a semantics (in ZF set theory) within which the logic is sound. We then provide an interpretation for (a rational reconstruction of) the specification language Z within ZC. As a result we obtain a sound logic for Z, including a basic schema calculus
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