Logicism and Logical Truth

1982 ◽  
Vol 79 (11) ◽  
pp. 692 ◽  
Author(s):  
Warren D. Goldfarb
Keyword(s):  
Logical Truth

Security of Cyber-Physical Systems: A Generalized Algorithm for Intrusion Detection and Determining Security Robustness of Cyber Physical Systems using Logical Truth Tables

2013 ◽  
Vol 9 ◽  
Author(s):  
Curtis G. Northcutt
Keyword(s):  
Intrusion Detection ◽  
Cyber Security ◽  
Logical Truth ◽  
Cyber Physical Systems ◽  
Security Model ◽  
Security Measures ◽  
Physical Systems ◽  
Multiple Signal ◽  
Security Attack ◽  
Truth Tables

The recent proliferation of embedded cyber components in modern physical systems [1] has generated a variety of new security risks which threaten not only cyberspace, but our physical environment as well. Whereas earlier security threats resided primarily in cyberspace, the increasing marriage of digital technology with mechanical systems in cyber-physical systems (CPS), suggests the need for more advanced generalized CPS security measures. To address this problem, in this paper we consider the first step toward an improved security model: detecting the security attack. Using logical truth tables, we have developed a generalized algorithm for intrusion detection in CPS for systems which can be defined over discrete set of valued states. Additionally, a robustness algorithm is given which determines the level of security of a discrete-valued CPS against varying combinations of multiple signal alterations. These algorithms, when coupled with encryption keys which disallow multiple signal alteration, provide for a generalized security methodology for both cyber-security and cyber-physical systems.

Quine, Strawson and logical truth

1973 ◽  
Vol 24 (1) ◽  
pp. 52-56 ◽  
Author(s):  
Marion Deckert
Keyword(s):  
Logical Truth

scholarly journals Hilary Putnam on the philosophy of logic and mathematics

2018 ◽  
Vol 33 (2) ◽  
pp. 183
Author(s):  
José Miguel Sagüillo Fernández-Vega
Keyword(s):  
Final Section ◽  
Mathematical Practice ◽  
Logical Truth ◽  
Hilary Putnam ◽  
Philosophy Of Logic ◽  
Logical Validity ◽  
And Mathematics

I discuss Putnam’s conception of logical truth as grounded in his picture of mathematical practice and ontology. i begin by comparing Putnam’s 1971 Philosophy of Logic with Quine’s homonymous book. Next, Putnam’s changing views on modality are surveyed, moving from the modal pre-formal to the de-modalized formal characterization of logical validity. Section three suggests a complementary view of Platonism and modalism underlying different stages of a dynamic mathematical practice. The final section argues for the pervasive platonistic conception of the working mathematician.

scholarly journals A Theory of Satisfiability-Preserving Proofs in SAT Solving

10.29007/tc7q ◽  
2018 ◽  
Author(s):  
Adrián Rebola-Pardo ◽  
Martin Suda
Keyword(s):  
Propositional Logic ◽  
Logical Truth ◽  
Point Of View ◽  
Traditional View ◽  
Satisfiability Problem ◽  
Sat Solving ◽  
Sat Solvers ◽  
Proof Systems ◽  
Meta Level

We study the semantics of propositional interference-based proof systems such as DRAT and DPR. These are characterized by modifying a CNF formula in ways that preserve satisfiability but not necessarily logical truth. We propose an extension of propositional logic called overwrite logic with a new construct which captures the meta-level reasoning behind interferences. We analyze this new logic from the point of view of expressivity and complexity, showing that while greater expressivity is achieved, the satisfiability problem for overwrite logic is essentially as hard as SAT, and can be reduced in a way that is well-behaved for modern SAT solvers. We also show that DRAT and DPR proofs can be seen as overwrite logic proofs which preserve logical truth. This much stronger invariant than the mere satisfiability preservation maintained by the traditional view gives us better understanding on these practically important proof systems. Finally, we showcase this better understanding by finding intrinsic limitations in interference-based proof systems.

The anatytic conception of truth and the foundations of arithmetic

2000 ◽  
Vol 65 (1) ◽  
pp. 33-102 ◽  
Author(s):  
Peter Apostoli
Keyword(s):  
Philosophy Of Mathematics ◽  
Logical Truth ◽  
Numerical Identity ◽  
Hume’S Principle ◽  
Contextual Definition ◽  
Definition Of ◽  
Axiomatic Set Theory ◽  
In Virtue Of ◽  
Second Order Logic ◽  
Foundations Of Arithmetic

Until very recently, it was thought that there couldn't be any current interest in logicism as a philosophy of mathematics. Indeed, there is an old argument one often finds that logicism is a simple nonstarter just in virtue of the fact that if it were a logical truth that there are infinitely many natural numbers, then this would be in conflict with the existence of finite models. It is certainly true that from the perspective of model theory, arithmetic cannot be a part of logic. However, it is equally true that model theory's reliance on a background of axiomatic set theory renders it unable to match Frege's Theorem, the derivation within second order logic of the infinity of the number series from the contextual “definition” of the cardinality operator. Called “Hume's Principle” by Boolos, the contextual definition of the cardinality operator is presented in Section 63 of Grundlagen, as the statement that, for any concepts F and G,the number of F s = the number of G sif, and only if,F is equinumerous with G.The philosophical interest in Frege's Theorem derives from the thesis, defended for example by Crispin Wright, that Hume's principle expresses our pre-analytic conception of assertions of numerical identity. However, Boolos cites the very fact that Hume's principle has only infinite models as grounds for denying that it is logically true: For Boolos, Hume's principle is simply a disguised axiom of infinity.

An Ancient Tradition

2017 ◽  
Author(s):  
Jan von Plato
Keyword(s):  
Nineteenth Century ◽  
Logical Truth ◽  
Great Circle ◽  
Hypothetical Reasoning ◽  
The Earth

This chapter talks about how the discovery of non-Euclidean geometries in the nineteenth century changed the traditional picture of axioms as evident truths: If triangles are drawn on the surface of the Earth so that each side is a part of a great circle (one that passes through two opposite points of the globe), the geometry is elliptic, and the sum of the angles of triangles is greater than that of two right angles. Axioms are now just some postulates that scholars choose as a basis. For some reason, today's logic did not first follow the lead of geometry, as a theory of hypothetical reasoning from axioms, but was formulated as a theory of logical truth on which even truth in mathematics was to be based.

The Nature of Logic

2019 ◽  
pp. 192-230
Author(s):  
Sanford Shieh
Keyword(s):  
Logical Truth

How does Frege conceive of logic, if not in modal terms? For Frege, logic is a system of truths that divides into primitive truths, which are axioms or basic laws, and logical truths justified by primitive logical truths. Frege appears to hold that what makes a thought a primitive logical truth is that it provides its own justification. However, Frege appears also to give arguments for the basic laws of Frege’s systems of logic. I argue that these arguments cannot be understood as non-question-begging demonstrations that the basic laws are self-justifying. Knowledge of self-justification results from the exercise of a perception-like capacity, and Frege’s “arguments” are intended to provide his readers with the occasion to exercise this capacity with respect to the thoughts expressed by his basic logical laws.

On the Idea of Logical Truth (I)

2017 ◽  
pp. 22-43
Author(s):  
Georg Henrik von Wright
Keyword(s):  
Logical Truth
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