Results 1 
8 of
8
Diamonds are a Philosopher's Best Friends. The Knowability Paradox and Modal Epistemic Relevance Logic (Extended Abstract)
 Journal of Philosophical Logic
, 2002
"... Heinrich Wansing Dresden University of Technology The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
Heinrich Wansing Dresden University of Technology The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is derived that all truths are, in fact, known. Nevertheless, the solution o#ered is in the spirit of the constructivist attitude usually maintained by defenders of the antirealist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete.
Implicit Programming and the Logic of Constructible Duality
, 1998
"... We present an investigation of duality in the traditional logical manner. We extend Nelson's symmetrization of intuitionistic logic, constructible falsity, to a selfdual logic constructible duality. We develop a selfdual model by considering an interval of worlds in an intuitionistic Kripk ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
We present an investigation of duality in the traditional logical manner. We extend Nelson's symmetrization of intuitionistic logic, constructible falsity, to a selfdual logic constructible duality. We develop a selfdual model by considering an interval of worlds in an intuitionistic Kripke model. The duality arises through how we judge truth and falsity. Truth is judged forward in the Kripke model, as in intuitionistic logic, while falsity is judged backwards. We develop a selfdual algebra such that every point in the algebra is representable by some formula in the logic. This algebra arises as an instantiation of a Heyting algebra into several categorical constructions. In particular, we show that this algebra is an instantiation of the Chu construction applied to a Heyting algebra, the second Dialectica construction applied to a Heyting algebra, and as an algebra for the study of recursion and corecursion. Thus the algebra provides a common base for these constructions, and suggests itself as an important part of any constructive logical treatment of duality. Implicit programming is suggested as a new paradigm for computing with constructible duality as its formal system. We show that all the operators that have computable least fixed points are definable explicitly and all operators with computable optimal fixed points are definable implicitly within constructible duality. Implicit programming adds a novel definitional mechanism that allows functions to be defined implicitly. This new programming feature is especially useful for programming with corecursively defined datatypes such as circular lists.
COMBINING INTUITIONISTIC CONNECTIVES AND ROUTLEY NEGATION
"... Abstract. Logic N ∗ was defined as a logical framework for studying deductive bases of the well founded semantics (WFS) of logics programs with negation. Its semantical definition combines Kripke frames for intuitionistic logic with Routley’s ∗operator, which is used to interpret the negation oper ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. Logic N ∗ was defined as a logical framework for studying deductive bases of the well founded semantics (WFS) of logics programs with negation. Its semantical definition combines Kripke frames for intuitionistic logic with Routley’s ∗operator, which is used to interpret the negation operation. In this paper we develop algebraic semantics for N∗, describe its subdirectly irreducible algebraic models, describe completely the lattice of normal HT 2extensions. The logic HT 2 is a finite valued extension of N∗, which is a deductive base of WFS. The last result can be used to check the maximality of this deductive base.
Preventing Conflict Situations During Authorization
"... Abstract: Computerbased access control systems working with financial and privacy issues are concerned with access control policies. Structuring authorizations turns out to be of a key importance in a case of collaborating organizations. Key–Words: Computerbased access control systems 1 ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract: Computerbased access control systems working with financial and privacy issues are concerned with access control policies. Structuring authorizations turns out to be of a key importance in a case of collaborating organizations. Key–Words: Computerbased access control systems 1
Preliminary Conference Proceedings
, 2004
"... or by other means) of all or part of this work is permitted for educational or research purposes only, on condition that (1) this copyright notice is included, (2) proper attribution to the author or authors is made, (3) no commercial gain is involved, and (4) the document is reproduced without any ..."
Abstract
 Add to MetaCart
(Show Context)
or by other means) of all or part of this work is permitted for educational or research purposes only, on condition that (1) this copyright notice is included, (2) proper attribution to the author or authors is made, (3) no commercial gain is involved, and (4) the document is reproduced without any alteration whatsoever.
A Note on Negation in Categorial
"... A version of strong negation is introduced into Categorial Grammar. The resulting syntactic calculi turn out to be systems of connexive logic. ..."
Abstract
 Add to MetaCart
(Show Context)
A version of strong negation is introduced into Categorial Grammar. The resulting syntactic calculi turn out to be systems of connexive logic.
A Variant of Thomason's Firstorder Logic CF Based On Situations
, 1997
"... In this paper, we define a firstorder logic CF 0 with strong negation and bounded classical quantifiers, which is a variant of Thomason's logic CF . For the logic CF 0 , the usual Kripke formal semantics is defined based on situations, and a sound and complete axiomatic system is estab ..."
Abstract
 Add to MetaCart
(Show Context)
In this paper, we define a firstorder logic CF 0 with strong negation and bounded classical quantifiers, which is a variant of Thomason's logic CF . For the logic CF 0 , the usual Kripke formal semantics is defined based on situations, and a sound and complete axiomatic system is established based on the axiomatic systems of constructive logics with strong negation and Thomason's completeness proof techniques. With the use of bounded quantifiers, CF 0 allows the domain of quantification to be empty and allows for nondenoting constants. CF 0 is intended as a fragment of a logic for situation theory. Thus the connection between CF 0 and infon logic is discussed. 1 Introduction In [23], Thomason constructed a firstorder logic CF . In his logic, a constructive negation is used instead of a classical or intuitionistic one. Constructive negation, also called strong negation, was introduced by D. Nelson in [20] following Kleene's notion of recursive realizability, empha...