scholarly journals Decidability of a Sound Set of Inference Rules for Computational Indistinguishability

2021 ◽  
Vol 22 (1) ◽  
pp. 1-44
Author(s):  
Adrien Koutsos
Keyword(s):  
Security Protocols ◽  
Term Rewriting ◽  
Automated Deduction ◽  
Inference Rules ◽  
Encryption Scheme ◽  
First Order ◽  
Bounded Number

Computational indistinguishability is a key property in cryptography and verification of security protocols. Current tools for proving it rely on cryptographic game transformations. We follow Bana and Comon’s approach [7, 8], axiomatizing what an adversary cannot distinguish. We prove the decidability of a set of first-order axioms that are computationally sound, though incomplete, for protocols with a bounded number of sessions whose security is based on an <small>IND-CCA 2 </small> encryption scheme. Alternatively, our result can be viewed as the decidability of a family of cryptographic game transformations. Our proof relies on term rewriting and automated deduction techniques.

Boolean-valued structures

2018 ◽  
Author(s):  
Tim Button ◽  
Sean Walsh
Keyword(s):  
Model Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Rules ◽  
Mathematical Concepts ◽  
Semantic Framework ◽  
First Order ◽  
Standard Models ◽  
Boolean Valued Model ◽  
Semantic Values

Chapters 6-12 are driven by questions about the ability to pin down mathematical entities and to articulate mathematical concepts. This chapter is driven by similar questions about the ability to pin down the semantic frameworks of language. It transpires that there are not just non-standard models, but non-standard ways of doing model theory itself. In more detail: whilst we normally outline a two-valued semantics which makes sentences True or False in a model, the inference rules for first-order logic are compatible with a four-valued semantics; or a semantics with countably many values; or what-have-you. The appropriate level of generality here is that of a Boolean-valued model, which we introduce. And the plurality of possible semantic values gives rise to perhaps the ‘deepest’ level of indeterminacy questions: How can humans pin down the semantic framework for their languages? We consider three different ways for inferentialists to respond to this question.

A new image encryption scheme based on a simple first-order time-delay system with appropriate nonlinearity

2015 ◽  
Vol 82 (1-2) ◽  
pp. 107-117 ◽  
Author(s):  
Olfa Mannai ◽  
Rabei Bechikh ◽  
Houcemeddine Hermassi ◽  
Rhouma Rhouma ◽  
Safya Belghith
Keyword(s):  
Time Delay ◽  
Image Encryption ◽  
Delay System ◽  
Encryption Scheme ◽  
Time Delay System ◽  
First Order

LOGICAL CHARACTERIZATION OF RECOGNIZABLE SETS OF POLYNOMIALS OVER A FINITE FIELD

2011 ◽  
Vol 22 (07) ◽  
pp. 1549-1563 ◽  
Author(s):  
MICHEL RIGO ◽  
LAURENT WAXWEILER
Keyword(s):  
Finite Field ◽  
Order Theory ◽  
Ring Of Integers ◽  
First Order ◽  
Polynomial Coefficients ◽  
Bounded Number ◽  
First Order Theory ◽  
Ring Of Polynomials

The ring of integers and the ring of polynomials over a finite field share a lot of properties. Using a bounded number of polynomial coefficients, any polynomial can be decomposed as a linear combination of powers of a non-constant polynomial P playing the role of the base of the numeration. Having in mind the theorem of Cobham from 1969 about recognizable sets of integers, it is natural to study P-recognizable sets of polynomials. Based on the results obtained in the Ph.D. thesis of the second author, we study the logical characterization of such sets and related properties like decidability of the corresponding first-order theory.

Lifting propositional proof compression algorithms to first-order logic

2020 ◽  
Author(s):  
Jan Gorzny ◽  
Ezequiel Postan ◽  
Bruno Woltzenlogel Paleo
Keyword(s):  
Propositional Logic ◽  
Empirical Evaluation ◽  
Order Logic ◽  
Automated Deduction ◽  
First Order Logic ◽  
Compression Algorithms ◽  
International Conference ◽  
First Order ◽  
Theorem Provers ◽  
Resolution Proofs

Abstract Proofs are a key feature of modern propositional and first-order theorem provers. Proofs generated by such tools serve as explanations for unsatisfiability of statements. However, these explanations are complicated by proofs which are not necessarily as concise as possible. There are a wide variety of compression techniques for propositional resolution proofs but fewer compression techniques for first-order resolution proofs generated by automated theorem provers. This paper describes an approach to compressing first-order logic proofs based on lifting proof compression ideas used in propositional logic to first-order logic. The first approach lifted from propositional logic delays resolution with unit clauses, which are clauses that have a single literal. The second approach is partial regularization, which removes an inference $\eta $ when it is redundant in the sense that its pivot literal already occurs as the pivot of another inference in every path from $\eta $ to the root of the proof. This paper describes the generalization of the algorithms LowerUnits and RecyclePivotsWithIntersection (Fontaine et al.. Compression of propositional resolution proofs via partial regularization. In Automated Deduction—CADE-23—23rd International Conference on Automated Deduction, Wroclaw, Poland, July 31–August 5, 2011, p. 237--251. Springer, 2011) from propositional logic to first-order logic. The generalized algorithms compresses resolution proofs containing resolution and factoring inferences with unification. An empirical evaluation of these approaches is included.

scholarly journals ON EXISTENTIAL DECLARATIONS OF INDEPENDENCE IN IF LOGIC

2013 ◽  
Vol 6 (2) ◽  
pp. 254-280 ◽  
Author(s):  
FAUSTO BARBERO
Keyword(s):  
Expressive Power ◽  
Inference Rules ◽  
Declaration Of Independence ◽  
Truth Values ◽  
First Order ◽  
If Logic ◽  
Knowledge Memory ◽  
Special Classes

AbstractWe analyze the behaviour of declarations of independence between existential quantifiers in quantifier prefixes of Independence-Friendly (IF) sentences; we give a syntactical criterion to decide whether a sentence beginning with such prefix exists, such that its truth values may be affected by removal of the declaration of independence. We extend the result also to equilibrium semantics values for undetermined IF sentences.The main theorem defines a schema of sound and recursive inference rules; we show more explicitly what happens for some simple special classes of sentences.In the last section, we extend the main result beyond the scope of prenex sentences, in order to give a proof of the fact that the fragment of IF sentences with knowledge memory has only first-order expressive power.

On the formalisation of indirect discourse

1958 ◽  
Vol 23 (4) ◽  
pp. 417-419 ◽  
Author(s):  
R. L. Goodstein
Keyword(s):  
Predicate Logic ◽  
Logical Truth ◽  
Predicate Calculus ◽  
Inference Rules ◽  
First Order ◽  
Indirect Discourse ◽  
Image Position ◽  
Order Predicate Calculus

Mr. L. J. Cohen's interesting example of a logical truth of indirect discourse appears to be capable of a simple formalisation and proof in a variant of first order predicate calculus. His example has the form:If A says that anything which B says is false, and B says that something which A says is true, then something which A says is false and something which B says is true.Let ‘A says x’ be formalised by ‘A(x)’ and let assertions of truth and falsehood be formalised as in the following table.We treat both variables x and predicates A (x) as sentences and add to the familiar axioms and inference rules of predicate logic a rule permitting the inference of A(p) from (x)A(x), where p is a closed sentence.We have to prove that from

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