Results 1  10
of
93
A Framework for Defining Logics
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1993
"... The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of ariti ..."
Abstract

Cited by 807 (45 self)
 Add to MetaCart
The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of arities. The treatment of rules and proofs focuses on his notion of a judgement. Logics are represented in LF via a new principle, the judgements as types principle, whereby each judgement is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurrence conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higherorder judgements and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logicindependent tools such as proof editors and proof checkers can be constructed.
Logic in Computer Science: Modelling and Reasoning about Systems
, 1999
"... ion. ACM Transactions on Programming Languages and Systems, 16(5):15121542, September 1994. Bibliography 401 [Che80] B. F. Chellas. Modal Logic  an Introduction. Cambridge University Press, 1980. [Dam96] D. R. Dams. Abstract Interpretation and Partition Refinement for Model Checking. PhD thesi ..."
Abstract

Cited by 345 (11 self)
 Add to MetaCart
ion. ACM Transactions on Programming Languages and Systems, 16(5):15121542, September 1994. Bibliography 401 [Che80] B. F. Chellas. Modal Logic  an Introduction. Cambridge University Press, 1980. [Dam96] D. R. Dams. Abstract Interpretation and Partition Refinement for Model Checking. PhD thesis, Institute for Programming research and Algorithmics. Eindhoven University of Technology, July 1996. [Dij76] E. W. Dijkstra. A Discipline of Programming. Prentice Hall, 1976. [DP96] R. Davies and F. Pfenning. A Modal Analysis of Staged Computation. In 23rd Annual ACM Symposium on Principles of Programming Languages. ACM Press, January 1996. [EN94] R. Elmasri and S. B. Navathe. Fundamentals of Database Systems. Benjamin/Cummings, 1994. [FHMV95] Ronald Fagin, Joseph Y. Halpern, Yoram Moses, and Moshe Y. Vardi. Reasoning about Knowledge. MIT Press, Cambridge, 1995. [Fit93] M. Fitting. Basic modal logic. In D. Gabbay, C. Hogger, and J. Robinson, editors, Handbook of Logic in Artificial In...
A Judgmental Reconstruction of Modal Logic
 Mathematical Structures in Computer Science
, 1999
"... this paper we reconsider the foundations of modal logic, following MartinL of's methodology of distinguishing judgments from propositions [ML85]. We give constructive meaning explanations for necessity (2) and possibility (3). This exercise yields a simple and uniform system of natural deductio ..."
Abstract

Cited by 195 (48 self)
 Add to MetaCart
this paper we reconsider the foundations of modal logic, following MartinL of's methodology of distinguishing judgments from propositions [ML85]. We give constructive meaning explanations for necessity (2) and possibility (3). This exercise yields a simple and uniform system of natural deduction for intuitionistic modal logic which does not exhibit anomalies found in other proposals. We also give a new presentation of lax logic [FM97] and find that it is already contained in modal logic, using the decomposition of the lax modality fl A as
Grammatical Framework: A TypeTheoretical Grammar Formalism
, 2003
"... Grammatical Framework (GF) is a specialpurpose functional language for defining grammars. It uses a Logical Framework (LF) for a description of abstract syntax, and adds to this a notation for defining concrete syntax. GF grammars themselves are purely declarative, but can be used both for lineariz ..."
Abstract

Cited by 101 (23 self)
 Add to MetaCart
Grammatical Framework (GF) is a specialpurpose functional language for defining grammars. It uses a Logical Framework (LF) for a description of abstract syntax, and adds to this a notation for defining concrete syntax. GF grammars themselves are purely declarative, but can be used both for linearizing syntax trees and parsing strings. GF can describe both formal and natural languages. The key notion of this description is a grammatical object, which is not just a string, but a record that contains all information on inflection and inherent grammatical features such as number and gender in natural languages, or precedence in formal languages. Grammatical objects have a type system, which helps to eliminate runtime errors in language processing. In the same way as an LF, GF uses...
Using State Space Exploration and a Natural Deduction Style Message Derivation Engine to Verify Security Protocols
 In Proc. IFIP Working Conference on Programming Concepts and Methods (PROCOMET
, 1998
"... As more resources are added to computer networks, and as more vendors look to the World Wide Web as a viable marketplace, the importance of being able to restrict access and to insure some kind of acceptable behavior even in the presence of malicious adversaries becomes paramount. Many researchers h ..."
Abstract

Cited by 81 (5 self)
 Add to MetaCart
(Show Context)
As more resources are added to computer networks, and as more vendors look to the World Wide Web as a viable marketplace, the importance of being able to restrict access and to insure some kind of acceptable behavior even in the presence of malicious adversaries becomes paramount. Many researchers have proposed the use of security protocols to provide these security guarantees. In this paper, we develop a method of verifying these protocols using a special purpose model checker which executes an exhaustive state space search of a protocol model. Our tool also includes a natural deduction style derivation engine which models the capabilities of the adversary trying to attack the protocol. Because our models are necessarily abstractions, we cannot prove a protocol correct. However, our tool is extremely useful as a debugger. We have used our tool to analyze 14 different authentication protocols, and have found the previously reported attacks for them. Keywords Model checking, security ...
Some lambda calculus and type theory formalized
 Journal of Automated Reasoning
, 1999
"... Abstract. We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified, proof of standardization for beta reduction, that does not mention ..."
Abstract

Cited by 65 (10 self)
 Add to MetaCart
(Show Context)
Abstract. We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified, proof of standardization for beta reduction, that does not mention redex positions or residuals. Then we outline the meta theory of Pure Type Systems, leading to the strengthening lemma. One novelty is our use of named variables for the formalization. Along the way we point out what we feel has been learned about general issues of formalizing mathematics, emphasizing the search for formal definitions that are convenient for formal proof and convincingly represent the intended informal concepts.
Query Answering in Information Systems with Integrity Constraints
, 1997
"... The specifications of most of the nowadays ubiquitous informations systems include integrity constraints, i.e. conditions rejecting socalled "invalid" or "inconsistent " data. Information system consistency and query answering have been formalized referring to classical logic im ..."
Abstract

Cited by 37 (0 self)
 Add to MetaCart
The specifications of most of the nowadays ubiquitous informations systems include integrity constraints, i.e. conditions rejecting socalled "invalid" or "inconsistent " data. Information system consistency and query answering have been formalized referring to classical logic implicitly assuming that query answering only makes sense with consistent information systems. In practice, however, inconsistent as well as consistent information systems need to be queried. In this paper, it is first argued that classical logic is inappropriate for a formalization of information systems because of its global notion of inconsistency. It is claimed that information systems inconsistency should be understood as a local notion. Then, it is shown that minimal logic, a constructivistic weakening of classical logic which precludes refutation proofs, provides for local inconsistencies that conveniently reflect a practitioner's intuition. Further, minimal logic is shown to be a convenient foundation fo...
The Feasibility of Defeat in Defeasible Reasoning
 In Proceedings of the 1st International Conference on Knowledge Representation and Reasoning
, 1991
"... Systems of defeasible reasoning are characterized by defeasible proofs, called arguments. I claim that sensible criteria of defeat among arguments in those systems are feasible, be it to a certain extent. As defeat eventually becomes unenforceable, the only option left is to pursue both arguments co ..."
Abstract

Cited by 28 (3 self)
 Add to MetaCart
Systems of defeasible reasoning are characterized by defeasible proofs, called arguments. I claim that sensible criteria of defeat among arguments in those systems are feasible, be it to a certain extent. As defeat eventually becomes unenforceable, the only option left is to pursue both arguments concurrently. This paper tries to confine the reach of defeat among arguments by means of several case studies, some of which are taken from the literature. 1. INTRODUCTION Reasoning beyond the information enclosed in the premises is a tempting but risky activity. It is tempting, because sheer deductive reasoning brings us no more than what was already recorded in the premises. And it is risky, because we might jump to the wrong conclusions. This is, very briefly, the issue of ampliative inference mechanisms. Ampliative inference can be defined as the result of rational nondeterministic nonmonotonic reasoning (Loui, 1990). The term itself is suggested by the American philosopher Peirce (183...