The enduring scandal of deduction

  title={The enduring scandal of deduction},
  author={Marcello D'Agostino and L. Floridi},
Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable… 
Tractable Depth-Bounded Logics and the Problem of Logical Omniscience
According to the standard logic of knowledge (epistemic logic) and belief, as well as to the more recent attempts to axiomatize the “logic of being informed” (information logic), if an agent i knows, or believes, or is informed that a sentence A is true, then i is supposed to know, or believe, or be informed also that B is true.
Information closure and the sceptical objection
It is argued that the sceptical objection against pic fails, so such an objection provides no ground to abandon the normal modal logic B as a formalization of “S is informed that $$p$$p”, which remains plausible insofar as this specific obstacle is concerned.
Informational Semantics, Non-Deterministic Matrices and Feasible Deduction
The Scandal of Deduction and Aristotle’s Method for Discovering Syllogisms
Abstract (1) If a deductive argument is valid, then the conclusion is not novel. (2) If the conclusion of an argument is not novel, the argument is not useful. So, (3) if a deductive argument is
The Paradox of Inference and the Non-Triviality of Analytic Information
The main thesis is that constructions are the vehicles of information, in the shape of constructions prescribing how to arrive at the truths in question, and even though analytically equivalent sentences have equal empirical content, their analytic content may be different.
Normality, Non-contamination and Logical Depth in Classical Natural Deduction
In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard
Strong Paraconsistency by Separating Composition and Decomposition in Classical Logic
A proof system is elaborate that is able to prove all classical first order logic consequences of consistent premise sets, without proving trivial consequences of inconsistent premises, and defines a very strong non-transitive paraconsistent logic.
Metalogic and the Overgeneration Argument
A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part
Semantics and proof-theory of depth bounded Boolean logics
A Modal View on Resource-Bounded Propositional Logics
  • Pere Pardo
  • Philosophy, Computer Science
    Studia Logica
  • 2022
This paper first study a hierarchy of tractable logics that is not defined by depth, then extends it into a modal logic where modalities make explicit the assumptions discharged in propositional proofs, thereby expressing blueprints for proofs.


Analytic natural deduction
The authors' completeness theorem for natural deduction uses as a counterpart to Konig's lemma, a lemma on infinite “nest structures”, as they are to be defined, as the underlying combinatorial basis of a wide variety of natural deduction systems.
Tableau Methods for Classical Propositional Logic
The deducibility problem of classical propositional logic was already ‘closed’ in the early 1920’s, when Wittgenstein and Post independently devised the well-known decision procedure based on the truth-tables.
The Scandal of Deduction
This article provides the first comprehensive reconstruction and analysis of Hintikka’s attempt to obtain a measure of the information yield of deductive inferences, and demonstrates that his attempt to provide such an account fails.
Towards Polynomial Approximations of Full Propositional Logic
  • M. Finger
  • Philosophy, Computer Science
  • 2004
This paper provides a family of logics, called Limited Bivaluation Logics, via a semantic approach to approximation that applies to full classical logic and shows that it performs at least as well as Dalal’s polynomial approach over clausal logic.
Cut and Pay
It is shown that there are families in which every component logic can be decided polynomially and one of these families is shown to possess the uniform substitution property, a new result for approximated reasoning.
Tractable Reasoning via Approximation
A Non-Deterministic Semantics for Tractable Inference
This work proposes a 3-valued semantics for a tractable fragment of propositional logic that is inherently non-deterministic: theDenotation of a formula is not uniquely determined by the denotation of the variables it contains.
The complexity of theorem-proving procedures
  • S. Cook
  • Mathematics, Computer Science
  • 1971
It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a
The logical basis of metaphysics
Michael Dummett's new book is the greatly expanded and recently revised version of his distinguished William James Lectures, delivered in 1976, and shows how the choice between different logics arises at the level of the theory of meaning and depends upon the choice of one or another general form of meaning-theory.
Polynomial Approximations of Full Propositional Logic via Limited Bivalence
An anytime family of logics that approximates classical inference, in which every step in the approximation can be decided in polynomial time is studied.