Related papers: A formal system for Euclid's Elements
This article provides formal definitions characterizing well-formed composition of components in order to guarantee their safe deployment and execution. Our work focuses on the structural aspects of component composition; it puts together…
In this paper we present a tableau proof system for first order logic of proofs FOLP. We show that the tableau system is sound and complete with respect to Mkrtychev models of FOLP.
This paper expands upon the finite state machine approach for the formal analysis of digital evidence. The proposed method may be used to support the feasibility of a given statement by testing it against a relevant system model. To achieve…
In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models…
The Edinburgh Logical Framework (LF) is a dependently type lambda calculus that can be used to encode formal systems. The versatility of LF allows specifications to be constructed also about the encoded systems. The Twelf system exploits…
This chapter provides an introduction to some basic concepts of epistemic logic, basic formal languages, their semantics, and proof systems. It also contains an overview of the handbook, and a brief history of epistemic logic and pointers…
Humans engage in informal debates on a daily basis. By expressing their opinions and ideas in an argumentative fashion, they are able to gain a deeper understanding of a given problem and in some cases, find the best possible course of…
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…
e-Motions is an Eclipse-based visual timed model transformation framework with a Real-Time Maude semantics that supports the usual Maude formal analysis methods, including simulation, reachability analysis, and LTL model checking. e-Motions…
The present paper provides an analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics. Dynamic epistemic logic is one of the best known members of a family of logical systems which…
The use of formal methods provides confidence in the correctness of developments. Yet one may argue about the actual level of confidence obtained when the method itself -- or its implementation -- is not formally checked. We address this…
In this note we give a wellfoundedness proof of a computable notation system for first-order reflection.
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
ECLAIR is a Prolog-based prototype system aiming to provide a functionally complete environment for the study, development and evaluation of programming language analysis and implementation tools. In this paper, we sketch the overall…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
We go into the need for, and the requirements on, a formal theory of budgets. We present a simple algebraic theory of rational budgets, i.e., budgets in which amounts of money are specified by functions on the rational numbers. This theory…
The formal system lambda-delta is a typed lambda calculus that pursues the unification of terms, types, environments and contexts as the main goal. lambda-delta takes some features from the Automath-related lambda calculi and some from the…
An observable canonical form is formulated for the set of rational systems on a variety each of which is a single-input-single-output, affine in the input, and a minimal realization of its response map. The equivalence relation for the…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
In this paper, we introduce a mathematical structure called Euclidean Universe. This structure provides a basic framework for Non-Archimedean Mathematics and in particular for Nonstandard Analysis.