• 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… 

Figures from this paper

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

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

Under Lock and Key: A Proof System for a Multimodal Logic

The modal fragment is almost always inspired by a Kripke semantics, and lacks a proof system, which precludes the immediate formulation of a well-behaved, computational theory for these logics under the Curry-Howard correspondence.

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

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.

Unification of Modal Logic via Topological Categories I

In this paper, we provide a unifying description of different types of semantics for modal logic found in the literature, using the language of topological categories (overSet). Just like in

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
...

References

SHOWING 1-10 OF 71 REFERENCES

Modal logic

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

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.

Modal logic and invariance

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

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.

Epistemic logic for AI and computer science

  • J. MeyerW. Hoek
  • Education, Philosophy
    Cambridge tracts in theoretical computer science
  • 1995
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.

SEMANTICAL CONSIDERATIONS ON FLOYD-HOARE LOGIC

  • V. Pratt
  • Computer Science, Philosophy
    FOCS 1976
  • 1976
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

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.

Logics of Time and Computation

Sets out the basic theory of normal modal and temporal propositional logics; applies this theory to logics of discrete (integer), dense (rational), and continuous (real) time, to the temporal logic

The metatheory of the classical propositional calculus is not axiomatizable

  • Ian A. Mason
  • Philosophy, Mathematics
    Journal of Symbolic Logic
  • 1985
It is proved that the first order metatheory of the classical propositional logic is undecidable and this result answers negatively a question of J. K. van Benthem as to whether the interpolation theorem in some sense completes the metatheories of the calculus.
...