Logical framework

Abstract: 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 l-calculus with dependent types. Syntax is treated in a style similar to, but more general than, Martin-Lo¨f's system of arities. The treatment of rules and proofs focuses on his notion of a judgment. Logics are represented in LF via a new principle, the judgments as types principle, whereby each judgment is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurence conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higher-order judgments and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logic-independent tools, such as proof editors and proof checkers, can be constructed.

Abstract: 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 l-calculus with dependent types. Syntax is treated in a style similar to, but more general than, Martin-Lo¨f's system of arities. The treatment of rules and proofs focuses on his notion of a judgment. Logics are represented in LF via a new principle, the judgments as types principle, whereby each judgment is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurence conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higher-order judgments and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logic-independent tools, such as proof editors and proof checkers, can be constructed.

Abstract: Motivation: To understand the behaviour of complex biological regulatory networks, a proper integration of molecular data into a full-fledge formal dynamical model is ultimately required. As most available data on regulatory interactions are qualitative, logical modelling offers an interesting framework to delineate the main dynamical properties of the underlying networks. Results: Transposing a generic model of the core network controlling the mammalian cell cycle into the logical framework, we compare different strategies to explore its dynamical properties. In particular, we assess the respective advantages and limits of synchronous versus asynchronous updating assumptions to delineate the asymptotical behaviour of regulatory networks. Furthermore, we propose several intermediate strategies to optimize the computation of asymptotical properties depending on available knowledge. Availability: The mammalian cell cycle model is available in a dedicated XML format (GINML) on our website, along with our logical simulation software GINsim ( ). Higher resolution state transitions graphs are also found on this web site (Model Repository page). Contact: thieffry@ibdm.univ-mrs.fr

Abstract: A LOGICAL FRAMEWORK FOR CATEGORIZING HIGHWAY SAFETY PHENOMENA AND ACTIVITY WILLIAM HADDON; The Journal of Trauma: Injury, Infection, and Critical Care