Pure Modal Logic of Names and Tableau Systems

  title={Pure Modal Logic of Names and Tableau Systems},
  author={A. Pietruszczak and Tomasz Jarmuzek},
  journal={Studia Logica},
By a pure modal logic of names (PMLN) we mean a quantifier-free formulation of such a logic which includes not only traditional categorical, but also modal categorical sentences with modalities de re and which is an extension of Propositional Logic. For categorical sentences we use two interpretations: a “natural” one; and Johnson and Thomason’s interpretation, which is suitable for some reconstructions of Aristotelian modal syllogistic (Johnson in Notre Dame J Form Logic 30(2):271–284, 1989… Expand
3 Citations
On Logic of Strictly-Deontic Modalities. A Semantic and Tableau Approach
This work sets forth a logic which additionally takes into consideration whether sentences stand in relation to the normative system or to the system of values under which the authors predicate the deontic qualifications, and arrives at a logical system which preserves laws proper to aDeontic logic but where the standard paradoxes of deontics logic do not arise. Expand
Aristotle's Syllogistic as a Deductive System
The essential elements of the Aristotelian system of syllogistic and Łukasiewicz’s reconstruction of it based on the tools of modern formal logic are discussed, with special attention to the notion of completeness of a deductive system. Expand
Knowability as De Re Modality: A Certain Solution to Fitch Paradox
Fitch paradox or Fitch-Church paradox, as it may also be called (see SALERNO 2009), is often considered as an argument against anti-realism. Accepting that every truth is knowable, as anti-realistsExpand


On Minimal Models for Pure Calculi of Names
By pure calculus of names we mean a quantifier-free theory, based on the classical propositional calculus, which defines predicates known from Aristotle’s syllogistic and Leśniewski’s Ontology. For aExpand
Cardinalities of Models and the Expressive Power of Monadic Predicate Logic (with Equality and Individual Constants)
It is proved that for any monadic formula φ: φ is logically valid iffπ is true in every interpretation whose domain contains at most l + 2 · n members. Expand
Models for Modal Syllogisms
  • F. A. Johnson
  • Philosophy, Computer Science
  • Notre Dame J. Formal Log.
  • 1989
A semantics is presented for Storrs McCalΓs separate axiomatiza- tions of Aristotle's accepted and rejected polysyllogisms, which treats syllogisms formed from assertoric and apodeictic propositions. Expand
Semantic analysis of the modal syllogistic
It is easy to understand Aristotle's assertoric syllogistic: an argument is valid if and only if every interpretation of the terms as non-vacuous predicates that makes the premisses true also makesExpand
An Axiomatisation of a Pure Calculus of Names
It is shown that the axiomatisation of a pure calculus of names is complete in three different ways: with respect to a set theoretical model, withrespect to Leśniewski's Ontology and in a sense defined with the use of axiomatic rejection. Expand
Relational Models for the Modal Syllogistic*
An interpretation of Aristotle’s modal syllogistic is proposed which is intuitively graspable, if only formally correst, and likely to be determined in a uniform way by the set of individuals to which the term necessarily-applies. Expand
An introduction to non-classical logic
Introduction 1. Classical logic and the material conditional 2. Basic modal logic 3. Normal modal logics 4. Non-normal worlds strict conditionals 5. Conditional logics 6. Intuitionist logic 7.Expand
An Introduction to Non-Classical Logic: From If to Is
  • 2008
Cardinalities of Models for Pure Calculi of Names
Aristotle's modal syllogisms