To Teach Modal Logic: An Opinionated Survey

I aim to promote an alternative agenda for teaching modal logic chiefly inspired by the relationships between modal logic and philosophy. The guiding idea for this proposal is a reappraisal of the interest of modal logic in philosophy, which do not stem mainly from mathematical issues, but which is motivated by central problems of philosophy and language. I will point out some themes to start elaborating a guide for a more comprehensive approach to teach modal logic, and consider the contributions of dual-process theories in cognitive science, in order to explore a pedagogical framework for the proposed point of view.Comment: Proceedings of the Fourth International Conference on Tools for Teaching Logic (TTL2015), Rennes, France, June 9-12, 2015. Editors: M. Antonia Huertas, Jo\~ao Marcos, Mar\'ia Manzano, Sophie Pinchinat, Fran\c{c}ois Schwarzentrube

Graphical Encoding of a Spatial Logic for the pi-Calculus

This paper extends our graph-based approach to the verification of spatial properties of π-calculus specifications. The mechanism is based on an encoding for mobile calculi where each process is mapped into a graph (with interfaces) such that the denotation is fully abstract with respect to the usual structural congruence, i.e., two processes are equivalent exactly when the corresponding encodings yield isomorphic graphs. Behavioral and structural properties of π-calculus processes expressed in a spatial logic can then be verified on the graphical encoding of a process rather than on its textual representation. In this paper we introduce a modal logic for graphs and define a translation of spatial formulae such that a process verifies a spatial formula exactly when its graphical representation verifies the translated modal graph formula

Modal Logic - a Tool for Design Process Formalisation

In this paper we show the possibility to formalize the design process by means of one type of non-standard logic - modal logic [1]. The type chosen for this study is modal logic S4. The reason for this choice is the ability of this formalism to describe modeling of the individual discrete steps of design, respecting necessity or possibility types of design knowledge

Modal Logic and the Approximation Induction Principle

We prove a compactness theorem in the context of Hennessy-Milner logic. It is used to derive a sufficient condition on modal characterizations for the Approximation Induction Principle to be sound modulo the corresponding process equivalence. We show that this condition is necessary when the equivalence in question is compositional with respect to the projection operators

Model-Checking the Higher-Dimensional Modal mu-Calculus

The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in polynomial time, and conversely every polynomial-time decidable problem that has a bisimulation-invariant encoding into labeled transition systems can also be defined in the higher-dimensional modal mu-calculus. We exemplify the latter connection by giving several examples of decision problems which reduce to model checking of the higher-dimensional modal mu-calculus for some fixed formulas. This way generic model checking algorithms for the logic can then be used via partial evaluation in order to obtain algorithms for theses problems which may benefit from improvements that are well-established in the field of program verification, namely on-the-fly and symbolic techniques. The aim of this work is to extend such techniques to other fields as well, here exemplarily done for process equivalences, automata theory, parsing, string problems, and games.Comment: In Proceedings FICS 2012, arXiv:1202.317

Blade loss transient dynamics analysis. Volume 3: User's manual for TETRA program

The users manual for TETRA contains program logic, flow charts, error messages, input sheets, modeling instructions, option descriptions, input variable descriptions, and demonstration problems. The process of obtaining a NASTRAN 17.5 generated modal input file for TETRA is also described with a worked sample

Making Theorem-Proving in Modal Logic Easy

A system for the modal logic K furnishes a simple mechanical process for proving theorems