599 research outputs found
Automated Synthesis of Tableau Calculi
This paper presents a method for synthesising sound and complete tableau
calculi. Given a specification of the formal semantics of a logic, the method
generates a set of tableau inference rules that can then be used to reason
within the logic. The method guarantees that the generated rules form a
calculus which is sound and constructively complete. If the logic can be shown
to admit finite filtration with respect to a well-defined first-order semantics
then adding a general blocking mechanism provides a terminating tableau
calculus. The process of generating tableau rules can be completely automated
and produces, together with the blocking mechanism, an automated procedure for
generating tableau decision procedures. For illustration we show the
workability of the approach for a description logic with transitive roles and
propositional intuitionistic logic.Comment: 32 page
Proceedings of the Joint Automated Reasoning Workshop and Deduktionstreffen: As part of the Vienna Summer of Logic – IJCAR 23-24 July 2014
Preface
For many years the British and the German automated reasoning communities have successfully run independent series of workshops for anybody working in the area of automated reasoning. Although open to the general
public they addressed in the past primarily the British and the German communities, respectively. At the occasion of the Vienna Summer of Logic the two series have a joint event in Vienna as an IJCAR workshop. In the spirit of the two series there will be only informal proceedings with abstracts of the works presented. These are collected in this document. We have tried to maintain the informal open atmosphere of the two series and have welcomed in particular research students to present their work. We have solicited for all work related to automated reasoning and its applications with a particular interest in work-in-progress and the presentation of half-baked ideas.
As in the previous years, we have aimed to bring together researchers from all areas of automated reasoning in order to foster links among researchers from various disciplines; among theoreticians, implementers and users alike, and among international communities, this year not just the British and German communities
Forward refutation for Gödel-Dummett Logics
We propose a refutation calculus to check the unprovability of a formula in Gödel-Dummett logics. From refutations we can directly extract countermodels for unprovable formulas, moreover the calculus is designed so to support a forward proof-search strategy that can be understood as a top-down construction of a model
Applying Formal Methods to Networking: Theory, Techniques and Applications
Despite its great importance, modern network infrastructure is remarkable for
the lack of rigor in its engineering. The Internet which began as a research
experiment was never designed to handle the users and applications it hosts
today. The lack of formalization of the Internet architecture meant limited
abstractions and modularity, especially for the control and management planes,
thus requiring for every new need a new protocol built from scratch. This led
to an unwieldy ossified Internet architecture resistant to any attempts at
formal verification, and an Internet culture where expediency and pragmatism
are favored over formal correctness. Fortunately, recent work in the space of
clean slate Internet design---especially, the software defined networking (SDN)
paradigm---offers the Internet community another chance to develop the right
kind of architecture and abstractions. This has also led to a great resurgence
in interest of applying formal methods to specification, verification, and
synthesis of networking protocols and applications. In this paper, we present a
self-contained tutorial of the formidable amount of work that has been done in
formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial
Theorem proving for non-normal modal logics
In this work we briefly summarize our recent contributions in the field of proof methods, theorem proving and countermodel generation for non-normal modal logics. We first recall some labelled sequent calculi for the basic system E and its extensions with axioms M, N, and C based on bi-neighbourhood semantics. Then, we present PRONOM, a theorem prover and countermodel generator for non-normal modal logics implemented in Prolog. When a modal formula is valid, then PRONOM computes a proof in the labelled calculi, otherwise it is able to extract a model falsifying it from an open, saturated branch. © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).Peer reviewe
Hypersequent calculi for non-normal modal and deontic logics: Countermodels and optimal complexity
We present some hypersequent calculi for all systems of the classical cube
and their extensions with axioms , , , and, for every , rule
. The calculi are internal as they only employ the language of the
logic, plus additional structural connectives. We show that the calculi are
complete with respect to the corresponding axiomatisation by a syntactic proof
of cut elimination. Then we define a terminating root-first proof search
strategy based on the hypersequent calculi and show that it is optimal for
coNP-complete logics. Moreover, we obtain that from every saturated leaf of a
failed proof it is possible to define a countermodel of the root hypersequent
in the bi-neighbourhood semantics, and for regular logics also in the
relational semantics. We finish the paper by giving a translation between
hypersequent rule applications and derivations in a labelled system for the
classical cube
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