Dialogical Connexive Logic

  title={Dialogical Connexive Logic},
  author={Shahid Rahman and Helge R{\"u}ckert},
Many of the discussions about conditionals can best be put as follows:can those conditionals that involve an entailment relation be formulatedwithin a formal system? The reasons for the failure of the classical approachto entailment have usually been that they ignore the meaning connectionbetween antecedent and consequent in a valid entailment. One of the firsttheories in the history of logic about meaning connection resulted from thestoic discussions on tightening the relation between the If… 

On Dialogues and Natural Deduction

The dialogical approach to logic has well known relations with other proof methods, like sequent calculi and semantic tableaux. In this paper we explore the connection between dialogues and natural

Argumentation and Abduction in Dialogical Logic

This chapter advocates for a reconciliation of argumentation theory and formal logic in an agent-centered theory of reasoning, that is, a theory in which inferences are studied as human activities.

A History Of Connexivity

  • S. McCall
  • Philosophy
    Logic: A History of its Central Concepts
  • 2012

Introducing consistency in a dialogical framework for paraconsistent logic

This paper reconstructs two logics of formal inconsistency tolerant to some amount of contradiction, but in which some versions of explosion still hold, and opens a new line of study on these logics, in the context of the game-theoretical approach to semantics born in the 1960s.

Dialogues as a Dynamic Framework for Logic

Dialogical logic is a game-theoretical approach to logic. Logic is studied with the help of certain games, which can be thought of as idealized argumentations. Two players, the Proponent, who puts

Epistemic and Practical Aspects of Conditionals in Leibniz's Legal Theory of Conditions

It is shown how Leibniz’s legal theory of conditions, by putting forward the notion of conditional, achieves to provide new answers to those very questions to provide a complete analysis of moral conditionals.

When Conditional Logic met Connexive Logic

This work presents the first formal system which allows modeling the ideas behind conditional logic and connexive logic in a unique framework and allows explaining the different ways conditionals are negated in natural language.

On Hypothetical Judgements and Leibniz’s Notion of Conditional Right

Sebastien Magnier provides a remarkable analysis of the notion of conditional right with the help of public announcement logic that he generalizes for the logical study of legal norms. Magnier’s main

Logics for Dialogue

It seems that the Game-Theoretic interpretation of Linear Logic provides the appropriate tool for combining elementary games of various kinds.

Inconsistency-Adaptive Dialogical Logic

The machinery of Batens’ approach is used to extend the paraconsistent approach to dialogical logic as developed by Rahman and Carnielli to obtain a dynamic mechanism for the systematic study of dialogues in which two parties exchange arguments over a central claim, in the possible presence of inconsistencies.



The Success of Failure The concept of failure in dialogue logics and its relevance for NL-semantics

It is shown how systems of formalized discussion that show the same logical behaviour as standard logical systems can be build and how such a system with additional fail operator can be used for the treatment of phenomena that are also relevant for natural language discourse.

Dialogues and Ontology, the Dialogical Approach to Free Logic

Being a pragmatic and not a referential approach to semantics, dialogi-cal logic does not understand semantics as mapping names, propositions and relationships into the real world to obtain an

The Dialogical Approach to Paraconsistency

A new, dialogical, way is shown touild paraconsistent systems for propositional and first-order logic with classical and intuitionistic features (i.e. paraconsistency both with and withouttertium non-datur) and present their corresponding tableaux.

On Frege's Nightmare: A Combination of Intuitionistic, Free and Paraconsistent Logics

In this paper I present a dialogical formulation of free logic which allows a straightforward combination of paraconsistent and intuitionistic logic-I call this combination Frege's Nightmare. The

Ways of understanding hugh Maccoll's concept of symbolic existence

Hugh MacColl (1837-1909) proposed, in several papers, a non-standard way of understanding the ontology underlying what we today call quantified propositions. His ideas, mixed with reflections about

A propositional logic with subjunctive conditionals

In this paper a formalized logic of propositions, P A1, is presented and its relationships to traditional logic, to PM ([15]), to subjunctive (including contrary-to-fact) implication and to the “paradoxes” of material and strict implication are developed.

Aristotle's modal syllogisms

  • F. Johnson
  • Philosophy
    Greek, Indian and Arabic Logic
  • 2001

Modal Provability Foundations for Negation by Failure

This paper presents a view of negation by failure as a modal provability notion, which makes the connection with the notion of Modal Provability, which is a well known, well established area of pure logic.

Formal systems of dialogue rules

Section 1 contains a survey of options in constructing a formal system of dialogue rules. The distinction between material and formal systems is discussed (section 1.1). It is stressed that the

Symbolic Logic

MR. McCOLL still expresses surprise at my declining to answer a Yes or No question which he was pleased to put to me in NATURE (vol. xxiv. p. 124). It was, I should think, almost unique in a