English
Related papers

Related papers: Primal implication as encryption

200 papers

Reconciling the tension between inductive learning and deductive reasoning in first-order relational domains is a longstanding challenge in AI. We study the problem of answering queries in a first-order relational probabilistic logic…

Artificial Intelligence · Computer Science 2026-02-17 Luise Ge , Brendan Juba , Kris Nilsson , Alison Shao

We prove two (strong) undefinability results for logics based on inquisitive semantics (or its variant, team semantics). Namely: 1) we show the undefinability of intuitionistic implication in extended propositional inquisitive logic with…

Logic · Mathematics 2024-07-31 Fausto Barbero

An important open question in AI is what simple and natural principle enables a machine to reason logically for meaningful abstraction with grounded symbols. This paper explores a conceptually new approach to combining probabilistic…

Artificial Intelligence · Computer Science 2025-02-20 Hiroyuki Kido

We examine the interplay between projectivity (in the sense that was introduced by S.~Ghilardi) and uniform post-interpolant for the classical and intuitionistic propositional logic. More precisely, we explore whether a projective…

Logic · Mathematics 2024-04-02 Mojtaba Mojtahedi , Konstantinos Papafilippou

Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…

Programming Languages · Computer Science 2020-07-21 Gilles Barthe , Justin Hsu , Kevin Liao

At CRYPTO 2013, Boneh and Zhandry initiated the study of quantum-secure encryption. They proposed first indistinguishability definitions for the quantum world where the actual indistinguishability only holds for classical messages, and they…

Cryptography and Security · Computer Science 2017-01-24 Tommaso Gagliardoni , Andreas Hülsing , Christian Schaffner

We produce a decidable super-intuitionistic normal modal logic of internalised intuitionistic (and thus disjunctive and monotonic) interactive proofs (LIiP) from an existing classical counterpart of classical monotonic non-disjunctive…

Logic · Mathematics 2015-09-22 Simon Kramer

We consider the problem EnumIP of enumerating prime implicants of Boolean functions represented by decision decomposable negation normal form (dec-DNNF) circuits. We study EnumIP from dec-DNNF within the framework of enumeration complexity…

Artificial Intelligence · Computer Science 2023-02-01 Alexis de Colnet , Pierre Marquis

The logic of bunched implications (BI) can be seen as the free combination of intuitionistic propositional logic (IPL) and intuitionistic multiplicative linear logic (IMLL). We present here a base-extension semantics (B-eS) for BI in the…

Logic in Computer Science · Computer Science 2024-11-12 Tao Gu , Alexander V. Gheorghiu , David J. Pym

Sandqvist gave a proof-theoretic semantics (P-tS) for classical logic (CL) that explicates the meaning of the connectives without assuming bivalance. Later, he gave a semantics for intuitionistic propositional logic (IPL). While soundness…

Logic · Mathematics 2025-07-18 Alexander V. Gheorghiu

This work is a mathematician's attempt to understand intuitionistic logic. It can be read in two ways: as a research paper interspersed with lengthy digressions into rethinking of standard material; or as an elementary (but highly…

Logic · Mathematics 2017-05-02 Sergey A. Melikhov

A common objection to the definition of intuitionistic implication in the Proof Interpretation is that it is impredicative. I discuss the history of that objection, argue that in Brouwer's writings predicativity of implication is ensured…

History and Overview · Mathematics 2018-05-08 Mark van Atten

We establish completeness for intuitionistic first-order logic, iFOL, showing that a formula is provable if and only if its embedding into minimal logic, mFOL, is uniformly valid under the Brouwer Heyting Kolmogorov (BHK) semantics, the…

Logic in Computer Science · Computer Science 2016-11-01 Robert Constable , Mark Bickford

Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…

Artificial Intelligence · Computer Science 2025-05-08 Luise Ge , Brendan Juba , Kris Nilsson

Human communication is based on a variety of inferences that we draw from sentences, often going beyond what is literally said. While there is wide agreement on the basic distinction between entailment, implicature, and presupposition, the…

Computation and Language · Computer Science 2024-05-10 Polina Tsvilodub , Paul Marty , Sonia Ramotowska , Jacopo Romoli , Michael Franke

An obfuscator is an algorithm that translates circuits into functionally-equivalent similarly-sized circuits that are hard to understand. Efficient obfuscators would have many applications in cryptography. Until recently, theoretical…

Cryptography and Security · Computer Science 2017-10-11 Gorjan Alagic , Stacey Jeffery , Stephen P. Jordan

This paper extends implication-space semantics to include first-order quantification. Implication-space semantics has recently been introduced as an inferentialist formal semantics that can capture nonmonotonic and nontransitive material…

Logic · Mathematics 2026-02-17 Ulf Hlobil

Recently, several public key exchange protocols based on symbolic computation in non-commutative (semi)groups were proposed as a more efficient alternative to well established protocols based on numeric computation. Notably, the protocols…

Group Theory · Mathematics 2016-09-07 Vladimir Shpilrain , Alexander Ushakov

Ensuring privacy during inference stage is crucial to prevent malicious third parties from reconstructing users' private inputs from outputs of public models. Despite a large body of literature on privacy preserving learning (which ensures…

Cryptography and Security · Computer Science 2024-12-02 Fengwei Tian , Ravi Tandon

A central question for causal inference is to decide whether a set of correlations fit a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for…

Quantum Physics · Physics 2018-07-26 Mirjam Weilenmann , Roger Colbeck