Results 1 
8 of
8
Propositional Lax Logic
, 1997
"... We investigate a novel intuitionistic modal logic, called Propositional Lax Logic, with promising applications to the formal verification of computer hardware. The logic has emerged from an attempt to express correctness `up to' behavioural constraints  a central notion in hardware verificat ..."
Abstract

Cited by 68 (8 self)
 Add to MetaCart
We investigate a novel intuitionistic modal logic, called Propositional Lax Logic, with promising applications to the formal verification of computer hardware. The logic has emerged from an attempt to express correctness `up to' behavioural constraints  a central notion in hardware verification  as a logical modality. The resulting logic is unorthodox in several respects. As a modal logic it is special since it features a single modal operator fl that has a flavour both of possibility and of necessity. As for hardware verification it is special since it is an intuitionistic rather than classical logic which so far has been the basis of the great majority of approaches. Finally, its models are unusual since they feature worlds with inconsistent information and furthermore the only frame condition is that the fl frame be a subrelation of the oeframe. In the paper we will provide the motivation for Propositional Lax Logic and present several technical results. We will investigate...
Jankov’s Theorems for Intermediate Logics in the Setting of Universal Models
"... In this article we prove the Jankov Theorem for extensions of IPC ([6]) and the Jankov Theorem for KC ([7]) in a uniform frametheoretic way in the setting of nuniversal models for IPC. In frametheoretic terms, the first Jankov Theorem states that for each finite rooted frame there is a formula ψ ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
In this article we prove the Jankov Theorem for extensions of IPC ([6]) and the Jankov Theorem for KC ([7]) in a uniform frametheoretic way in the setting of nuniversal models for IPC. In frametheoretic terms, the first Jankov Theorem states that for each finite rooted frame there is a formula ψ with the property that any countermodel for ψ needs this frame in the sense that each descriptive frame that falsifies ψ will have this frame as the pmorphic image of a generated subframe. The second one states that KC is the strongest logic that proves no negationless formulas beyond IPC. On the way we give a simple proof of the fact discussed and proved in [1] that the upper part of the nHenkin model H(n) is isomorphic to the nuniversal model U(n) of IPC. All these results earlier occurred in a somewhat different form in [8]. 1
INTERMEDIATE LOGICS AND THE DE JONGH PROPERTY
, 2009
"... Abstract. We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property. Dedicated to Petr Hájek, on the occasion of his 70th Birthday 1. Preface The three authors of this paper have enjoyed Petr Hájek’s acquaintance since the late e ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property. Dedicated to Petr Hájek, on the occasion of his 70th Birthday 1. Preface The three authors of this paper have enjoyed Petr Hájek’s acquaintance since the late eighties, when a lively community interested in the metamathematics of arithmetic shared ideas and traveled among the beautiful cities of Prague, Moscow, Amsterdam, Utrecht, Siena, Oxford and Manchester. At that time, Petr Hájek and Pavel Pudlák were writing their landmark book Metamathematics of FirstOrder Arithmetic [HP91], which Petr Hájek tried out on a small group of eager graduate students in Siena in the months of February and March 1989. Since then, Petr Hájek has been a role model to us in many ways. First of all, we have always been impressed by Petr’s meticulous and clear use of correct notation, witness all his different types of dots and corners, for example in the Tarskian ‘snowing’snowing lemmas [HP91]. But also as a human being, Petr has been a role model by his example of living in truth, even in averse circumstances [Hav89]. The tragic story of the Logic Colloquium 1980, which was planned to be held in Prague and of which Petr Hájek was the driving force, springs to mind [DvDLS82]. Finally, we were moved by Petr’s openmindedness when coming to terms with a situation that turned out to look disconcertingly unlike the ‘standard model ’ 1. Therefore, in this paper, we would like to pay homage to Petr Hájek. Unfortunately, we cannot hope to emulate his correct use of dots and corners. Instead, we do our best to provide some pleasing nonstandard models and nonclassical arithmetics. 2.
unknown title
, 2015
"... Preservation of admissible rules when combining logics ..."
(Show Context)
The rules of intermediate logic
"... For Dick de Jongh, on the occasion of his 65th birthday. If Visser’s rules are admissible for an intermediate logic, they form a basis for the admissible rules of the logic. How to characterize the admissible rules of intermediate logics for which not all of Visser’s rules are admissible is not know ..."
Abstract
 Add to MetaCart
(Show Context)
For Dick de Jongh, on the occasion of his 65th birthday. If Visser’s rules are admissible for an intermediate logic, they form a basis for the admissible rules of the logic. How to characterize the admissible rules of intermediate logics for which not all of Visser’s rules are admissible is not known. Here we study the situation for specific intermediate logics. We provide natural examples of logics for which Visser’s rule are derivable, admissible but nonderivable, or not admissible.
Unification in fragments of intermediate logics
, 2012
"... This paper contains a proof theoretic treatment of some aspects of unification in intermediate logics. It is shown that many existing results can be extended to fragments that at least contain implication and conjunction. For such fragments the connection between valuations and most general unifier ..."
Abstract
 Add to MetaCart
(Show Context)
This paper contains a proof theoretic treatment of some aspects of unification in intermediate logics. It is shown that many existing results can be extended to fragments that at least contain implication and conjunction. For such fragments the connection between valuations and most general unifiers is clarified, and it is shown how from the closure of a formula under the socalled Visser rules a proof of the formula under a projective unifier can be obtained. This implies that in the logics considered the admissibility of the nth Visser rule is a sufficient condition for the nunification type to be finitary. At the end of the paper it is shown how these results imply several wellknown results from the literature.