scholarly journals Pure Variable Inclusion Logics

2021 ◽  
pp. 1-22
Author(s):  
Francesco Paoli ◽  
Michele Pra Baldi ◽  
Damian Szmuc
Keyword(s):  
Classical Logic

The aim of this article is to discuss pure variable inclusion logics, that is, logical systems where valid entailments require that the propositional variables occurring in the conclusion are included among those appearing in the premises, or vice versa. We study the subsystems of Classical Logic satisfying these requirements and assess the extent to which it is possible to characterise them by means of a single logical matrix. In addition, we semantically describe both of these companions to Classical Logic in terms of appropriate matrix bundles and as semilattice-based logics, showing that the notion of consequence in these logics can be interpreted in terms of truth (or non-falsity) and meaningfulness (or meaninglessness) preservation. Finally, we use Płonka sums of matrices to investigate the pure variable inclusion companions of an arbitrary finitary logic.

New method for building ASP knowledge base from knowledge in classical logic

2010 ◽  
Vol 30 (11) ◽  
pp. 2932-2936
Author(s):  
Ling-zhong ZHAO ◽  
Xue-song WANG ◽  
Jun-yan QIAN ◽  
Guo-yong CAI
Keyword(s):  
Knowledge Base ◽  
Classical Logic ◽  
New Method

The Argument from Counterfactuals

2018 ◽  
Author(s):  
Alexander R. Pruss
Keyword(s):  
Natural Law ◽  
Classical Logic ◽  
Divine Command

It seems that counterfactuals and many other statements are subject to semantic underdetermination. Classical logic pushes one to an epistemicist account of this underdetermination, but epistemicism seems implausible. However epistemicism can be made plausible when conjoined with a divine institution account of meaning. This gives us some reason to accept that divine institution account, and hence some reason to think that God exists. This chapter evaluates the arguments for epistemicism and divine institution, including objections, and incorporates Plantinga’s consideration of counterfactuals when it comes to theism. In particular, an analogy is drawn with divine command and natural law theories in ethics.

The 10th IJCAR automated theorem proving system competition – CASC-J10

2021 ◽  
pp. 1-15
Author(s):  
Geoff Sutcliffe
Keyword(s):  
Theorem Proving ◽  
Classical Logic ◽  
Automated Theorem Proving ◽  
Fully Automatic

The CADE ATP System Competition (CASC) is the annual evaluation of fully automatic, classical logic Automated Theorem Proving (ATP) systems. CASC-J10 was the twenty-fifth competition in the CASC series. Twenty-four ATP systems and system variants competed in the various competition divisions. This paper presents an outline of the competition design, and a commentated summary of the results.

Y-Logic: A Framework for Reasoning About Chameleonic Programs with Inconsistent Completions

1990 ◽  
Vol 13 (4) ◽  
pp. 465-483
Author(s):  
V.S. Subrahmanian
Keyword(s):  
Classical Logic ◽  
Logic Program ◽  
Logic Programs ◽  
Large Subset ◽  
General Logic ◽  
Traditional Sense

Large logic programs are normally designed by teams of individuals, each of whom designs a subprogram. While each of these subprograms may have consistent completions, the logic program obtained by taking the union of these subprograms may not. However, the resulting program still serves a useful purpose, for a (possibly) very large subset of it still has a consistent completion. We argue that “small” inconsistencies may cause a logic program to have no models (in the traditional sense), even though it still serves some useful purpose. A semantics is developed in this paper for general logic programs which ascribes a very reasonable meaning to general logic programs irrespective of whether they have consistent (in the classical logic sense) completions.

scholarly journals On Correspondence between Selective CPS Transformation and Selective Double Negation Translation

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 385
Author(s):  
Hyeonseung Im
Keyword(s):  
Programming Languages ◽  
Intuitionistic Logic ◽  
Reference Point ◽  
Classical Logic ◽  
Proof System ◽  
Double Negation

A double negation translation (DNT) embeds classical logic into intuitionistic logic. Such translations correspond to continuation passing style (CPS) transformations in programming languages via the Curry-Howard isomorphism. A selective CPS transformation uses a type and effect system to selectively translate only nontrivial expressions possibly with computational effects into CPS functions. In this paper, we review the conventional call-by-value (CBV) CPS transformation and its corresponding DNT, and provide a logical account of a CBV selective CPS transformation by defining a selective DNT via the Curry-Howard isomorphism. By using an annotated proof system derived from the corresponding type and effect system, our selective DNT translates classical proofs into equivalent intuitionistic proofs, which are smaller than those obtained by the usual DNTs. We believe that our work can serve as a reference point for further study on the Curry-Howard isomorphism between CPS transformations and DNTs.

scholarly journals Traditional Logic and Computational Thinking

Philosophies ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 12
Author(s):  
J.-Martín Castro-Manzano
Keyword(s):  
Logic Programming ◽  
Classical Logic ◽  
Computational Thinking ◽  
Traditional Logic ◽  
Aristotelian Logic

In this contribution, we try to show that traditional Aristotelian logic can be useful (in a non-trivial way) for computational thinking. To achieve this objective, we argue in favor of two statements: (i) that traditional logic is not classical and (ii) that logic programming emanating from traditional logic is not classical logic programming.

Logic and Cognitive Science

Istoriya ◽  
2021 ◽  
Vol 12 (8 (106)) ◽  
pp. 0
Author(s):  
Natalia Zaitseva
Keyword(s):  
Cognitive Science ◽  
Classical Logic ◽  
Mutual Influence ◽  
Pure Logic ◽  
The Status ◽  
Experimental Logic ◽  
The Relationship

The paper examines the relationship between logic and cognitive science. We consider various aspects of this relationship, among which we distinguish three of the most importance, in our thought. First, it is the role of cognitive science in the justification of logic. Secondly, the mutual influence of cognitive science and modern trends of non-classical logic, which have a clearly applied character. Third, we discuss the prospects of the so-called experimental logic arising from attempts to apply the methods of cognitive science in logic. As usual, the conclusion summarizes the results of the research and focuses on the issue of the status of pure logic.

scholarly journals A Logic of Comparative Support: Qualitative Conditional Probability Relations Representable by Popper Functions

2017 ◽  
Author(s):  
James Hawthorne
Keyword(s):  
Probability Theory ◽  
Decision Theory ◽  
Classical Logic ◽  
Scientific Theory ◽  
Classical Probability ◽  
Open Questions ◽  
Classical Setting ◽  
Alternative Approaches ◽  
Popper Functions ◽  
Self Reference

Revising classical logic—to deal with the paradoxes of self-reference, or vague propositions, for the purposes of scientific theory or of metaphysical anti-realism—requires the revision of probability theory. This chapter reviews the connection between classical logic and classical probability, clarifies nonclassical logic, giving simple examples, explores modifications of probability theory, using formal analogies to the classical setting, and provides two foundational justifications for these ‘nonclassical probabilities’. There follows an examination of extensions of the nonclassical framework: to conditionalization and decision theory in particular, before a final review of open questions and alternative approaches, and an evaluation of current progress.

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