• Corpus ID: 62162288

Modal Logic for Open Minds

@inproceedings{Benthem2010ModalLF,
  title={Modal Logic for Open Minds},
  author={Johan van Benthem},
  year={2010}
}
In Modal Logic for Open Minds, Johan van Benthem provides an introduction to the field of modal logic, outlining its major ideas and exploring the numerous ways in which various academic fields have adopted it. Van Benthem begins with the basic theories of modal logic, examining its relationship to language, semantics, bisimulation, and axiomatics, and then covers more advanced topics, such as expressive power, computational complexity, and intelligent agency. Many of the chapters are followed… 
Possibility Frames and Forcing for Modal Logic
Possibility Frames and Forcing for Modal Logic ∗ Wesley H. Holliday Department of Philosophy & Group in Logic and the Methodology of Science University of California, Berkeley December 30, 2015
Term-Sequence-Modal Logics
TLDR
This paper expands term-modal logics by allowing a modal operator to be indexed by a finite sequence of terms as well as a single term, and provides sound Hilbert-style axiomatizations (without Barcan-like axioms) for the logics and establishes the strong completeness results for some of thelogics.
1 SEMANTIC PERSPECTIVES IN LOGIC
The pleasantly erudite and still highly readable paper Beth 1963 saw logic as consisting of three basic strands, historically entangled and complementary: linguistic definability (semantics, if you
A Sequent Calculus for K-restricted Common Sense Modal Predicate Logic
In recent years, Common sense Modal Predicate Calculus (CMPC) has been proposed by J. van Benthem in [4, pp. 120–121] and further developed by J. Seligman in [1, 3, 2]. It allows us to ‘take ∃ to
Belief contraction through safe formulas
1 In this paper we consider approaches to belief revision and contraction in modal logics that are based on a translation of an agent’s beliefs in modal logic to first-order logic, where revision or
A Lindström-style theorem for finitary propositional weak entailment languages with absurdity
TLDR
It is shown that the basic weak entailment model- theoretic language with absurdity is the maximal model-theoreticlanguage having the finite occurrence property, preservation under relevant directed bisimulations and the finite depth property.
One Modal Logic to Rule Them All?
TLDR
This logic enables a conceptual shift, as what have traditionally been called different “modal logics” now become [∀p]-universal theories over the base logic GQM: instead of defining a new logic with an axiom schema such as 2φ → 22φ, one reasons in G QM about what follows from the globally quantified formula [∄p](2p→ 22p).
Title One Modal Logic to Rule Them All ?
In this paper, we introduce an extension of the modal language with what we call the global quantificational modality [∀p]. In essence, this modality combines the propositional quantifier ∀p with the
Modal Logic for Artificial Intelligence
These course notes were written for an introduction in modal logic for students in Cognitive Artificial Intelligence at Utrecht University. Earlier notes by Rosalie Iemhoff have been used both as a
Logic and Commonsense Reasoning
These are the lecture notes of a course on logic and commonsense reasoning given to master students in philosophy of the University of Rennes 1. N.B.: Some parts of these lectures notes are sometimes
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 76 REFERENCES
Modal logic
TLDR
This paper shows how the tree or tableau method provides a simple and easily comprehensible decision procedure for systems such as K, T, S4 and S5 and how the formal techniques of modal logic can be used to analyse several informal problems involving modal concepts, including cases combining modality with quantification.
The Undecidability of Iterated Modal Relativization
TLDR
It is shown that for three fragments of the logic of iterated relativization and transitive closure, the satisfiability problems are fi1 Σ11–complete, and the question of whether a sentence in these fragments has a finite (tree) model is fi0 Σ01–complete.
Tools and Techniques in Modal Logic
Chapter Headings only. About this Book. Overview. Part 1. The Fundamentals. Algebra, logic and deduction. Fundamentals of modal logic I. Fundamentals of modal logic II. Part 2. The General Theory of
Modal logic and invariance
TLDR
This analysis yields a characterization of invariance and safety under bisimulation as natural conditions for logical operations in modal and dynamic logics, and some new transfer results between first-order logic and modal logic.
Modal Logics of Space
TLDR
The interest of Space remains intriguing – both for mathematical reasons, and given the amount of work in CS and AI on visual reasoning and image processing, which involves logic of spatial structures.
A General Semantics for Quantified Modal Logic
TLDR
This paper gives a complete semantics to the quantified extensions, both with and without the Barcan formula, of every proposi- tional modal logic S, and employs frames in which not every set of worlds is an admissible proposition.
Epistemic logic for AI and computer science
  • J. Meyer, W. Hoek
  • Computer Science
    Cambridge tracts in theoretical computer science
  • 1995
TLDR
This book, based on courses taught at universities and summer schools, provides a broad introduction to the subject and considers applications in the areas of common knowledge, distributed knowledge, explicit and implicit belief.
Modal Fixed-Point Logic and Changing Models
We show that propositional dynamic logic and the modal µ-calculus are closed under product modalities, as defined in current dynamic-epistemic logics. Our analysis clarifies the latter systems, while
SEMANTICAL CONSIDERATIONS ON FLOYD-HOARE LOGIC
TLDR
An appropriate axiom system is given which is complete for loop-free programs and also puts conventional predicate calculus in a different light by lumping quantifiers with non-logical assignments rather than treating them as logical concepts.
Lindstrom theorems for fragments of first-order logic
TLDR
This paper provides Lindstrom characterizations for a number of fragments of first-order logic, including the k-variable fragments for k > 2, Tarski's relation algebra, graded modal logic, and the binary guarded fragment, which imply semantic preservation theorems.
...
1
2
3
4
5
...