Type-Theoretical Dynamics

  title={Type-Theoretical Dynamics},
  author={Giuseppe Primiero},
  booktitle={The Realism-Antirealism Debate in the Age of Alternative Logics},
  • G. Primiero
  • Published in
    The Realism-Antirealism…
  • Economics
In the present paper a dynamics for type theory is introduced. The formalization provides epistemic explanations for the basic notions of belief state and belief set by referring to assertion conditions for type-theoretical judgements; it interprets expectations in terms of default assumptions for such a structure and it adapts the usual revision operations and the analogous of the Ramsey test. The model, restricted to operations of revision, merging and information preference, provides a… 


Realistic Belief Revision
It is shown that the standard representation theorems still hold for paraconsistent belief revision, and conditions under which consistency is preserved by revisions are given, which allows for the gradual revision of inconsistency.
Formalizing Belief Revision in Type Theory
This paper formalizes belief revision for belief states in type theory by proposing a procedure for identifying and removing "suspect" beliefs, and beliefs depending on them, and studying the belief change operations emerging from this perspective in the setting of typed lambda-calculus.
Belief revision in a framework for default reasoning
  • G. Brewka
  • Computer Science
    The Logic of Theory Change
  • 1989
We present an approach which provides a common solution to problems recently addressed in two different research areas: nonmonotonic reasoning and theory revision. We define a framework for default
On the logic of theory change: Partial meet contraction and revision functions
The authors investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated, and basic properties of these functions are established.
Majority merging by adaptive counting
A belief merging procedure by majority using the standard format of Adaptive Logics is introduced and is proven to be equivalent to a standard majority operator for bases with partial support.
Presuppositions , Assumptions , Premises ∗
In Martin-Löf’s Constructive Type Theory (CTT) judgements are given in terms of assertion conditions. They, in turn, furnish an account of the key notions of presupposition, assumption, and premise.
Introducing Justification into Epistemic Logic
This paper studies two basic systems, S4LP and S4LPN, of epistemic logic with justification, and shows completeness with respect to natural epistemic semantics, which augments Kripke models with a natural Fitting-style treatment of justification assertions t:F.
A Logical Framework for Default Reasoning
  • D. Poole
  • Computer Science, Philosophy
    Artif. Intell.
  • 1988
Belief Revision
This book contains a collection of up-to-date research articles on belief revision and an introductory chapter that presents a survey of current research in the area and the fundamentals of the theory.
Prioritized dynamic retraction function on non-monotonic information updates
A model for updates on prioritized belief sets and retractions thereof is introduced, using the standard format of Adaptive Logics, which aims at restricting the validity of formulas represented by abnormal expressions derivable in the language.