Related papers: Primal implication as encryption
In this paper, we show that the derivability problem for the primal propositional logic remains solvable in polynomial time upon adding a certain form of the principle of equivalent form substitution; and that, upon adding another form of…
In this paper we intend to study implications in their most general form, generalizing different classes of implications including the Heyting implication, sub-structural implications and weak strict implications. Following the topological…
We study the first-order primal infon logic. It is the core of the policy language DKAL. We provide Gentzen-style calculi for two versions of this logic that are not equivalent. For both versions we investigate the semantics: one of them is…
Oblivious transfer is a primitive of paramount importance in cryptography or, more precisely, two- and multi-party computation due to its universality. Unfortunately, oblivious transfer cannot be achieved in an unconditionally secure way…
When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them,…
A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…
The logic of bunched implications (BI), introduced by O'Hearn and Pym (1999), has attracted significant attention due to its elegant proof calculus, varied semantics, and close connections to the propositional fragment of separation logic.…
We answer a question of Paterson, showing that all block systems for the group generated by the round functions of a key-alternating block cipher are the translates of a linear subspace. Following up remarks of Paterson and Shamir, we…
Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…
In this paper we provide an algorithm for solving constrained composite primal-dual monotone inclusions, i.e., monotone inclusions in which a priori information on primal-dual solutions is represented via closed convex sets. The proposed…
In an impressive series of papers, Krivine showed at the edge of the last decade how classical realizability provides a surprising technique to build models for classical theories. In particular, he proved that classical realizability…
The approach taken by Gheorghiu, Gu and Pym in their paper on giving a Base-extension Semantics for Intuitionistic Multiplicative Linear Logic is an interesting adaptation of the work of Sandqvist for IPL to the substructural setting. What…
We study implicational formulas in the context of proof complexity of intuitionistic propositional logic (IPC). On the one hand, we give an efficient transformation of tautologies to implicational tautologies that preserves the lengths of…
Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algorithmic information theory. His central result is that the…
We consider algorithms for solving structured convex optimization problems over a network of agents with communication delays. It is assumed that each agent performs its local updates by using possibly outdated information from its…
In applications involving sensitive data, such as finance and healthcare, the necessity for preserving data privacy can be a significant barrier to machine learning model development. Differential privacy (DP) has emerged as one canonical…
We present a unified categorical treatment of completeness theorems for several classical and intuitionistic infinitary logics with a proposed axiomatization. This provides new completeness theorems and subsumes previous ones by G\"odel,…
Uncloneable encryption is a cryptographic primitive which encrypts a classical message into a quantum ciphertext, such that two quantum adversaries are limited in their capacity of being able to simultaneously decrypt, given the key and…
Logic $L$ was introduced by Lewitzka [7] as a modal system that combines intuitionistic and classical logic: $L$ is a conservative extension of CPC and it contains a copy of IPC via the embedding $\varphi\mapsto\square\varphi$. In this…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…