scholarly journals Logical omniscience and classical logic

2005 ◽  
pp. 52-64
Author(s):  
Reinhard Muskens
Keyword(s):  
Classical Logic ◽  
Logical Omniscience

Epistemic Logics

2019 ◽  
pp. 107-124
Author(s):  
Francesco Berto ◽  
Mark Jago
Keyword(s):  
Epistemic Logic ◽  
Classical Logic ◽  
Possible Worlds ◽  
Impossible Worlds ◽  
Logical Omniscience ◽  
Epistemic States ◽  
Deep Problem

Standard possible-worlds epistemic logic gives rise to the problem of logical omniscience. There are attempts to deal with the problem without using impossible worlds. A number of these approaches are discussed in this chapter and all are found wanting. The impossible worlds approach is immediately more successful, but faces a deep problem: how should impossible worlds be constrained, so as to give adequate models of knowledge and belief? One option is to take impossible worlds to be closed under some weaker-than-classical logic. But this approach does not genuinely solve the problem of logical omniscience. A different approach is the dynamic one, whereby epistemic states are not closed at any one time, but nevertheless evolve towards closure in a dynamic way.

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.

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