A Seligman-Style Tableau System

  title={A Seligman-Style Tableau System},
  author={Patrick Blackburn and Thomas Bolander and Torben Bra{\"u}ner and Klaus Frovin J{\o}rgensen},
Proof systems for hybrid logic typically use @-operators to access information hidden behind modalities; this labeling approach lies at the heart of most resolution, natural deduction, and tableau systems for hybrid logic. But there is another, less well-known approach, which we have come to believe is conceptually clearer. We call this Seligman-style inference, as it was first introduced and explored by Jerry Seligman in the setting of natural deduction and sequent calculus in the late 1990s… 

Completeness and termination for a Seligman-style tableau system

This paper develops a Seligman-style tableau system for basic hybrid logic and proves its completeness, and proves termination of a restricted version of the system without resorting to loop checking, and shows that the restrictions do not eect completeness.

Hybrid-Logical Reasoning in the Smarties and Sally-Anne Tasks

  • T. Braüner
  • Philosophy, Computer Science
    J. Log. Lang. Inf.
  • 2014
A proof system for hybrid modal logic is used to formalize what are called false-belief tasks in cognitive psychology, thereby investigating the interplay between cognition and logical reasoning about belief.



Internalizing labelled deduction

This paper shows how to internalize the Kripke satisfaction definition using the basic hybrid language and explores the proof theoretic consequences of doing so, and concludes with some reflections on the status of labelling in modal logic.

Two Natural Deduction Systems for Hybrid Logic: A Comparison

  • T. Braüner
  • Computer Science, Mathematics
    J. Log. Lang. Inf.
  • 2004
Two different natural deduction systems for hybrid logic are compared and contrasted, and a set of reduction rules is devised for the latter system by translation of already known reduction rules for the former system.

Tableau Calculi for Hybrid Logics

This work presents prefixed tableau calculi for weak hybrid logics (proper fragments of classical logic) as well as for hybridlogics having full first-order expressive power, and gives a general method for proving completeness.

On an Intuitionistic Modal Logic

This paper considers an intuitionistic variant of the modal logic S4 (which it is called IS4), and places particular importance on the natural deduction formulation of IS4— this formulation has several important metatheoretic properties.

Direct resolution for modal-like logics

A resolution calculus for hybrid logics addressing these problems: the hybrid machinery is used to “push formulas out of modalities” and in this way, feed them into a simple and standard resolution rule.

Hybrid Logic and its Proof-Theory

Preface,.- 1 Introduction to Hybrid Logic.- 2 Proof-Theory of Propositional Hybrid Logic .- 3 Tableaus and Decision Procedures for Hybrid Logic .- 4 Comparison to Seligman's Natural Deduction System

Indexical Hybrid Tense Logic

This paper introduces a special now nominal (the authors' @now corresponds to Kamp’s original now operator N) and proves completeness for the richer language, again for both logical and contextual validity.

Internalization: The Case of Hybrid Logics

The semantic theory of hybrid logic is formalized using a sequent calculus for predicate logic plus axioms, which is quite general and can be applied to a wide range of hybrid and modal logics.

Termination for Hybrid Tableaus

This article extends and improves work on tableau-based decision methods for hybrid logic by Bolander and Brauner and defines a internalised system which terminates without loop-checks, simpler than previously known internalised systems and simpler than the prefix systems.

A Hybrid Intuitionistic Logic: Semantics and Decidability

It is proved that the hybrid intuitionistic modal logic suitable for reasoning about distribution of resources is decidable and provides a sound and complete Kripke semantics and enjoys the finite model property.