Related papers: A Coinductive Version of Milner's Proof System for…
Full Intuitionistic Linear Logic (FILL) is multiplicative intuitionistic linear logic extended with par. Its proof theory has been notoriously difficult to get right, and existing sequent calculi all involve inference rules with complex…
Justification logics are modal-like logics that provide a framework for reasoning about justifications. This paper introduces labeled sequent calculi for justification logics, as well as for hybrid modal-justification logics. Using the…
We study the finitary version of the coalgebraic logic introduced by L. Moss. The syntax of this logic, which is introduced uniformly with respect to a coalgebraic type functor, required to preserve weak pullbacks, extends that of classical…
Scala's type system unifies ML modules, object-oriented, and functional programming. The Dependent Object Types (DOT) family of calculi has been proposed as a new foundation for Scala and similar languages. Unfortunately, it is not clear…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
We present an extension of the second-order logic AF2 with iso-style inductive and coinductive definitions specifically designed to extract programs from proofs a la Krivine-Parigot by means of primitive (co)recursion principles. Our logic…
This paper tackles the problem of formulating and proving the completeness of focused-like proof systems in an automated fashion. Focusing is a discipline on proofs which structures them into phases in order to reduce proof search…
A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…
This paper introduces a uniform substitution calculus for differential refinement logic dRL. The logic dRL extends the differential dynamic logic dL such that one can simultaneously reason about properties of and relations between hybrid…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
We study proof techniques for bisimilarity based on unique solution of equations. We draw inspiration from a result by Roscoe in the denotational setting of CSP and for failure semantics, essentially stating that an equation (or a system of…
The preferential conditional logic PCL, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalise Lewis' sphere models for counterfactual logics, is proposed. Soundness…
The proof of Brouwer's fixed-point theorem based on Sperner's lemma is often presented as an elementary combinatorial alternative to advanced proofs based on algebraic topology. The goal of this note is to show that: (i) the combinatorial…
We extend the work of A. Ciaffaglione and P. Di Gianantonio on mechanical verification of algorithms for exact computation on real numbers, using infinite streams of digits implemented as co-inductive types. Four aspects are studied: the…
Deductive methods for the verification of hybrid systems vary on the format of statements in correctness proofs. Building on the example of Hoare triple-based reasoning, we have investigated several such methods for systems described in…
Over extended systems of finite type arithmetic, we utilize a formal representation of the outer measure to define a translation which allows for the systematic formalization of probabilistic statements. As a main result, this translation…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
This paper introduces modal independence logic MIL, a modal logic that can explicitly talk about independence among propositional variables. Formulas of MIL are not evaluated in worlds but in sets of worlds, so called teams. In this vein,…
Introduced in 2006 by Japaridze, cirquent calculus is a refinement of sequent calculus. The advent of cirquent calculus arose from the need for a deductive system with a more explicit ability to reason about resources. Unlike the more…
We establish new, and surprisingly tight, connections between propositional proof complexity and finite model theory. Specifically, we show that the power of several propositional proof systems, such as Horn resolution, bounded-width…