Corpus ID: 235490610

Algebraic Semantics for the Logic of Proofs

  title={Algebraic Semantics for the Logic of Proofs},
  author={Amir Farahmand Parsa and Meghdad Ghari},
We present algebraic semantics for the classical logic of proofs based on Boolean algebras. We also extend the language of the logic of proofs in order to have a Boolean structure on proof terms and equality predicate on terms. Moreover, the completeness theorem and certain generalizations of Stone’s representation theorem are obtained for all proposed algebras. 


A Note on Some Explicit Modal Logics
Artemov introduced the Logic of Proofs (LP) as a logic of explicit proofs. We can also offer an epistemic reading of this formula: “t is a possible justification of φ”. Motivated, in part, by this
Models for the Logic of Proofs
A model for the operational logic of proofs is defined and the decidability of a variant of \(\mathcal{L}\mathcal {P}\)axiomatized by a finite set of schemes is proved.
Evidence Reconstruction of Epistemic Modal Logic S5
The language of Logic of Proofs LP is extended by a new unary operation of negative checker “?” and Kripke-style models for the resulting logic are defined in the style of Fitting models and the corresponding Completeness theorem is proved.
Explicit provability and constructive semantics
This paper finds the logic LP of propositions and proofs and shows that Godel's provability calculus is nothing but the forgetful projection of LP, which achievesGodel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which resisted formalization since the early 1930s.
The logic of proofs, semantically
  • M. Fitting
  • Computer Science
    Ann. Pure Appl. Log.
  • 2005
This semantics is used to give new proofs of several basic results concerning LP, and the realization of S4 into LP is established in a way that carefully examines and explicates the role of the + operator.
On Intermediate Justification Logics.
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we
The Ontology of Justifications in the Logical Setting
It is argued that justifications in the logical setting are naturally interpreted as sets of formulas which leads to a class of epistemic models that are called modular models.
Semirings of Evidence
This work presents a novel semantic approach to justification logic that models evidence by a semiring that provides an adequate semantics for evidence terms and clarifies the role of variables in justification logic.
Subset Models for Justification Logic
A new semantics for justification logic based on subset relations is introduced, which model justifications as sets of possible worlds and shows that they subsume Artemov's approach to aggregating probabilistic evidence.
A Syntactic Realization Theorem for Justification Logics
A syntactic proof of a single realization theorem that uniformly connects all the normal modal logics formed from the axioms with their justification counterparts by showing that the positive introspection operator is superfluous.