SOUNDNESS

In the literature, the conditions on history variables or forward simulations that are related to liveness are expressed in terms of behaviours, and are stronger than convenient and necessary. In this paper, we propose alternative conditions on the simulation relation, which are expressed in terms of the next state relation, and are closely tied to the weak or strong fairness conditions of the specifications. The proof of soundness of this proposal is based on a new theorem that asserts the existence of a strongly fair scheduler for infinitely many alternatives. The theory is extended to simulations in which the concrete specification (occasionally) does fewer steps than the abstract specification it implements.

A distributed storage service lets clients abstract a single reliable shared storage device using a collection of possibly unreliable computing units. Algorithms that implement this abstraction offer certain tradeoffs and vary according to dimensions such as complexity, the consistency semantics provided, and the types of failures tolerated.

This paper investigates the problem of inference channels that occur when databaseconstraints are combined with non-sensitive data to obtain sensitive information. Wepresent an integrated security mechanism, called the Disclosure Monitor, which guaranteesdata confidentiality by extending the standard mandatory access control mechanismwith a Disclosure Inference Engine. The Disclosure Inference Engine generates all theinformation that can be disclosed to a user based

Weaver, George and John Corcoran. 1974. Logical Consequence in Modal Logic II: Some Semantic Systems for S4, Notre Dame Journal of Formal Logic 15, 370–78.
ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis’s S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be equivalent; but, when regarded as consequence systems (ibid., p. 157), one diverges from the others in a fashion which suggests that two standard measures of semantic complexity may not be as closely linked as previously thought.

This 1974 paper uses the linear notation for natural deduction presented in [2]: each two-dimensional deduction is represented by a unique one-dimensional string of characters. Thus obviating need for two-dimensional trees, tableaus, lists, and the like—thereby facilitating electronic communication of natural deductions.
The 1969 paper presents a (modal, sentential) logic which may be thought of as a partial systematization of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of this logic coincides those of standard formalizations of Lewis’s S4. Among the paper's innovations is its treatment of modal logic in the setting of natural deduction systems--as opposed to axiomatic systems.
The author’s apologize for the now obsolete terminology. For example, these papers speak of “a proof of a sentence from a set of premises” where today “a deduction of a sentence from a set of premises” would be preferable.
1. Corcoran, John. 1969. Three Logical Theories, Philosophy of Science 36, 153–77. J P R

2. Corcoran, John and George Weaver. 1969. Logical Consequence in Modal Logic: Natural Deduction in S5 Notre Dame Journal of Formal Logic 10, 370–84. MR0249278 (40 #2524).
3. Weaver, George and John Corcoran. 1974. Logical Consequence in Modal Logic II: Some Semantic Systems for S4, Notre Dame Journal of Formal Logic 15, 370–78.  MR0351765 (50 #4253).

We introduce a reasoning infrastructure for proving statements about resource consumption in a fragment of the Java Virtual Machine Language (JVML). The infrastructure is based on a small hierarchy of program logics, with increasing levels of abstraction: at the top there is a type system for a high-level language that encodes resource consumption. The infrastructure is designed to be used in a proof-carrying code (PCC) scenario, where mobile programs can be equipped with formal evidence that they have predictable resource behaviour.This article focuses on the core logic in our infrastructure, a VDM-style program logic for partial correctness, which can make statements about resource consumption alongside functional behaviour. We establish some important results for this logic, including soundness and completeness with respect to a resource-aware operational semantics for the JVML. We also present a second logic built on top of the core logic, which is used to express termination; it too is shown to be sound and complete. We then outline how high-level language type systems may be connected to these logics.The entire infrastructure has been formalized in Isabelle/HOL, both to enhance the confidence in our meta-theoretical results, and to provide a prototype implementation for PCC. We give examples to show the usefulness of this approach, including proofs of resource bounds on code resulting from compiling high-level functional programs.