The Herbrand Award for Distinguished Contributions to Automated Reasoning is an award given by the Conference on Automated Deduction (CADE), Inc., (although it predates the formal incorporation of CADE) to honour persons or groups for important contributions to the field of automated deduction. The award is named after the French scientist Jacques Herbrand and given at most once per CADE or International Joint Conference on Automated Reasoning (IJCAR). It comes with a prize of US$1,000. Anyone can be nominated, the award is awarded after a vote among CADE trustees and former recipients, usually with input from the CADE/IJCAR programme committee. == Recipients == Past award recipients are: === 1990s === Larry Wos (1992) Woody Bledsoe (1994) John Alan Robinson (1996) Wu Wenjun (1997) Gérard Huet (1998) Robert S. Boyer and J Strother Moore (1999) === 2000s === William W. McCune (2000) Donald W. Loveland (2001) Mark E. Stickel (2002). Peter B. Andrews (2003) Harald Ganzinger (2004) Martin Davis (2005) Wolfgang Bibel (2006) Alan Bundy (2007) Edmund M. Clarke (2008) Deepak Kapur (2009) === 2010s === David Plaisted (2010) Nachum Dershowitz (2011) Melvin Fitting (2012) C. Greg Nelson (2013) Robert L. Constable (2014) Andrei Voronkov (2015) Zohar Manna and Richard Waldinger (2016) Lawrence C. Paulson (2017) Bruno Buchberger (2018) Nikolaj Bjørner and Leonardo de Moura (2019) === 2020s === Franz Baader (2020) Tobias Nipkow (2021) Natarajan Shankar (2022) Moshe Vardi (2023) Armin Biere (2024) Aart Middeldorp (2025)
Interactions Corporation
Interactions LLC (also known as Interactions Corporation) is an American software company that develops voice and text-based virtual assistant applications for customer-service contact centers. Since September 2025, it has been a subsidiary of SoundHound AI. == History == Interactions was founded in 2004. In July 2011, the company announced a $12 million venture-capital funding round led by Sigma Partners. In November 2014, AT&T sold its "Watson" speech recognition platform and related patents to Interactions in exchange for equity. In May 2017, Interactions acquired the social media customer-engagement company Digital Roots; financial terms were not disclosed. On September 3, 2025, SoundHound AI completed its acquisition of Interactions Corporation, with the acquired company becoming a wholly owned subsidiary. == Products and services == Interactions' products have been described as automated voice portals and intelligent virtual assistants used for customer-service tasks. In 2011, Humana expanded the use of an Interactions voice portal for Medicare Part D enrollment.
Document AI
Document AI, also known as Document Intelligence, refers to a field of technology that employs machine learning (ML) techniques, such as natural language processing (NLP). These techniques are used to develop computer models capable of analyzing documents in a manner akin to human review. Through NLP, computer systems are able to understand relationships and contextual nuances in document contents, which facilitates the extraction of information and insights. Additionally, this technology enables the categorization and organization of the documents themselves. The applications of Document AI extend to processing and parsing a variety of semi-structured documents, such as forms, tables, receipts, invoices, tax forms, contracts, loan agreements, and financial reports. == Key features == Machine learning is utilized in Document AI to extract information from both printed and digital documents. This technology recognizes images, text, and characters in various languages, aiding in the extraction of insights from unstructured documents. The use of this technology can improve the speed and quality of decision-making in document analysis. Additionally, the automation of data extraction and validation can contribute to increased efficiency in document analysis processes. Since the early 2020s, the integration of large language models has extended Document AI beyond extraction toward generative tasks, including the automated drafting of forms, contracts, and document summaries. == Example == A business letter contains information in the form of text, as well as other types of information, such as the position of the text. For instance, a typical letter contains two addresses before the body of the text. The address at the very top (sometimes aligned to the right) is the sender address. This is normally followed by the date of the letter, with the place of writing. After this, the receiver address is listed. The distinction between the sender address and the receiver address is conveyed solely by the position of the address on the page, i.e. there is no textual indication like Sender: in front of the addresses. == Data dimensions and ML architecture == Data is typically distinguished into spatial data and time-series data, the former includes things like images, maps and graphs, while the latter includes signals such as stock prices or voice recordings. Document AI combines text data, which has a time dimension, with other types of data, such as the position of an address in a business letter, which is spatial. Historically in machine learning spatial data was analyzed using a convolutional neural network, and temporal data using a recurrent neural network. With the advent of dimension-type agnostic transformer architecture, these two different types of dimension can be more easily combined, Document AI is an example of this. == Benchmarks == Several public datasets are used to evaluate Document AI systems. FUNSD (Form Understanding in Noisy Scanned Documents) contains 199 annotated forms with token- and block-level labels for form understanding tasks. CORD (Consolidated Receipt Dataset) supports key information extraction from receipts. DocVQA contains approximately 50,000 questions over 12,000 document images for layout-aware visual question answering. == Common uses == Document AI systems are used to automate document processing and information extraction in business and financial workflows, including invoice and receipt processing, data entry automation, anomaly detection, mortgage processing, loan portfolio monitoring, credit risk management, and fraud detection such as counterfeit currency and fraudulent checks. They are also applied in regulatory compliance and contract analysis, including assessing changes in legal and regulatory documents. In real estate, Document AI supports document classification and structured information extraction for standardized processing and analytics. With the adoption of generative AI, Document AI systems can also generate and pre-fill structured documents such as contracts or business forms from natural language prompts.
Thompson sampling
Thompson sampling, named after William R. Thompson, is a heuristic for choosing actions that address the exploration–exploitation dilemma in the multi-armed bandit problem. It consists of choosing the action that maximizes the expected reward with respect to a randomly drawn belief. == Description == Consider a set of contexts X {\displaystyle {\mathcal {X}}} , a set of actions A {\displaystyle {\mathcal {A}}} , and rewards in R {\displaystyle \mathbb {R} } . The aim of the player is to play actions under the various contexts, such as to maximize the cumulative rewards. Specifically, in each round, the player obtains a context x ∈ X {\displaystyle x\in {\mathcal {X}}} , plays an action a ∈ A {\displaystyle a\in {\mathcal {A}}} and receives a reward r ∈ R {\displaystyle r\in \mathbb {R} } following a distribution that depends on the context and the issued action. The elements of Thompson sampling are as follows: a likelihood function P ( r | θ , a , x ) {\displaystyle P(r|\theta ,a,x)} ; a set Θ {\displaystyle \Theta } of parameters θ {\displaystyle \theta } of the distribution of r {\displaystyle r} ; a prior distribution P ( θ ) {\displaystyle P(\theta )} on these parameters; past observations triplets D = { ( x ; a ; r ) } {\displaystyle {\mathcal {D}}=\{(x;a;r)\}} ; a posterior distribution P ( θ | D ) ∝ P ( D | θ ) P ( θ ) {\displaystyle P(\theta |{\mathcal {D}})\propto P({\mathcal {D}}|\theta )P(\theta )} , where P ( D | θ ) {\displaystyle P({\mathcal {D}}|\theta )} is the likelihood function. Thompson sampling consists of playing the action a ∗ ∈ A {\displaystyle a^{\ast }\in {\mathcal {A}}} according to the probability that it maximizes the expected reward; action a ∗ {\displaystyle a^{\ast }} is chosen with probability ∫ I [ E ( r | a ∗ , x , θ ) = max a ′ E ( r | a ′ , x , θ ) ] P ( θ | D ) d θ , {\displaystyle \int \mathbb {I} \left[\mathbb {E} (r|a^{\ast },x,\theta )=\max _{a'}\mathbb {E} (r|a',x,\theta )\right]P(\theta |{\mathcal {D}})d\theta ,} where I {\displaystyle \mathbb {I} } is the indicator function. In practice, the rule is implemented by sampling. In each round, parameters θ ∗ {\displaystyle \theta ^{\ast }} are sampled from the posterior P ( θ | D ) {\displaystyle P(\theta |{\mathcal {D}})} , and an action a ∗ {\displaystyle a^{\ast }} chosen that maximizes E [ r | θ ∗ , a ∗ , x ] {\displaystyle \mathbb {E} [r|\theta ^{\ast },a^{\ast },x]} , i.e. the expected reward given the sampled parameters, the action, and the current context. Conceptually, this means that the player instantiates their beliefs randomly in each round according to the posterior distribution, and then acts optimally according to them. In most practical applications, it is computationally onerous to maintain and sample from a posterior distribution over models. As such, Thompson sampling is often used in conjunction with approximate sampling techniques. == History == Thompson sampling was originally described by Thompson in 1933. It was subsequently rediscovered numerous times independently in the context of multi-armed bandit problems. A first proof of convergence for the bandit case has been shown in 1997. The first application to Markov decision processes was in 2000. A related approach (see Bayesian control rule) was published in 2010. In 2010 it was also shown that Thompson sampling is instantaneously self-correcting. Asymptotic convergence results for contextual bandits were published in 2011. Thompson Sampling has been widely used in many online learning problems including A/B testing in website design and online advertising, and accelerated learning in decentralized decision making. A Double Thompson Sampling (D-TS) algorithm has been proposed for dueling bandits, a variant of traditional MAB, where feedback comes in the form of pairwise comparison. == Relationship to other approaches == === Probability matching === Probability matching is a decision strategy in which predictions of class membership are proportional to the class base rates. Thus, if in the training set positive examples are observed 60% of the time, and negative examples are observed 40% of the time, the observer using a probability-matching strategy will predict (for unlabeled examples) a class label of "positive" on 60% of instances, and a class label of "negative" on 40% of instances. === Bayesian control rule === A generalization of Thompson sampling to arbitrary dynamical environments and causal structures, known as Bayesian control rule, has been shown to be the optimal solution to the adaptive coding problem with actions and observations. In this formulation, an agent is conceptualized as a mixture over a set of behaviours. As the agent interacts with its environment, it learns the causal properties and adopts the behaviour that minimizes the relative entropy to the behaviour with the best prediction of the environment's behaviour. If these behaviours have been chosen according to the maximum expected utility principle, then the asymptotic behaviour of the Bayesian control rule matches the asymptotic behaviour of the perfectly rational agent. The setup is as follows. Let a 1 , a 2 , … , a T {\displaystyle a_{1},a_{2},\ldots ,a_{T}} be the actions issued by an agent up to time T {\displaystyle T} , and let o 1 , o 2 , … , o T {\displaystyle o_{1},o_{2},\ldots ,o_{T}} be the observations gathered by the agent up to time T {\displaystyle T} . Then, the agent issues the action a T + 1 {\displaystyle a_{T+1}} with probability: P ( a T + 1 | a ^ 1 : T , o 1 : T ) , {\displaystyle P(a_{T+1}|{\hat {a}}_{1:T},o_{1:T}),} where the "hat"-notation a ^ t {\displaystyle {\hat {a}}_{t}} denotes the fact that a t {\displaystyle a_{t}} is a causal intervention (see Causality), and not an ordinary observation. If the agent holds beliefs θ ∈ Θ {\displaystyle \theta \in \Theta } over its behaviors, then the Bayesian control rule becomes P ( a T + 1 | a ^ 1 : T , o 1 : T ) = ∫ Θ P ( a T + 1 | θ , a ^ 1 : T , o 1 : T ) P ( θ | a ^ 1 : T , o 1 : T ) d θ {\displaystyle P(a_{T+1}|{\hat {a}}_{1:T},o_{1:T})=\int _{\Theta }P(a_{T+1}|\theta ,{\hat {a}}_{1:T},o_{1:T})P(\theta |{\hat {a}}_{1:T},o_{1:T})\,d\theta } , where P ( θ | a ^ 1 : T , o 1 : T ) {\displaystyle P(\theta |{\hat {a}}_{1:T},o_{1:T})} is the posterior distribution over the parameter θ {\displaystyle \theta } given actions a 1 : T {\displaystyle a_{1:T}} and observations o 1 : T {\displaystyle o_{1:T}} . In practice, the Bayesian control amounts to sampling, at each time step, a parameter θ ∗ {\displaystyle \theta ^{\ast }} from the posterior distribution P ( θ | a ^ 1 : T , o 1 : T ) {\displaystyle P(\theta |{\hat {a}}_{1:T},o_{1:T})} , where the posterior distribution is computed using Bayes' rule by only considering the (causal) likelihoods of the observations o 1 , o 2 , … , o T {\displaystyle o_{1},o_{2},\ldots ,o_{T}} and ignoring the (causal) likelihoods of the actions a 1 , a 2 , … , a T {\displaystyle a_{1},a_{2},\ldots ,a_{T}} , and then by sampling the action a T + 1 ∗ {\displaystyle a_{T+1}^{\ast }} from the action distribution P ( a T + 1 | θ ∗ , a ^ 1 : T , o 1 : T ) {\displaystyle P(a_{T+1}|\theta ^{\ast },{\hat {a}}_{1:T},o_{1:T})} . === Upper-confidence-bound (UCB) algorithms === Thompson sampling and upper-confidence bound algorithms share a fundamental property that underlies many of their theoretical guarantees. Roughly speaking, both algorithms allocate exploratory effort to actions that might be optimal and are in this sense "optimistic". Leveraging this property, one can translate regret bounds established for UCB algorithms to Bayesian regret bounds for Thompson sampling or unify regret analysis across both these algorithms and many classes of problems.
Lymphater's Formula
"Lymphater's Formula" (Polish: "Formula Lymphatera") is a 1961 science fiction short story by Polish writer Stanisław Lem. It is a story of a "mad scientist", mathematician Ammon Lymphater, who invents an artificial intelligence, and then he realizes that it is capable of rendering the humankind obsolete. It was first published in the 1961 collection Księga robotów (Book of Robots) with the pre-annotation "from the memoirs of Ijon Tichy". The story was never republished with this pre-annotation, and nothing in the novel gives any indication at Ijon Tichy. Piotr Krywak tried to figure out possible explanations for this, apart from a typographical error. == Plot == Ammon Lymphater became interested in the emerging science of cybernetics and information theory, and started studying the works of an animal brain, the ant's brain in particular. He took note that the inherited knowledge is an evolutionary advantage somehow not exploited in full by the evolution. Eventually he came to a conclusion that only by pure biological restrictions that adaptive abilities of insects were stopped in their tracks by the evolution. He went on further wondering whether the ants have an ability to apriori knowledge, i.e., knowledge neither inherited nor learned. He decided to consult a famous myrmecologist, who told him about a rare ant species Acanthis Rubra Willinsoniana with an exceptionally high adaptability. Eventually Lymphater devised and constructed "It" capable of instant precognition of everything within "Its" rapidly expanding range of perception. From "It" Lymphater learns that the humanity is not the "crown of evolution", but rather evolution's tool to create "It", because the evolution could not create "It" directly (confirming Lymphater's reasoning about ants). Realizing that the Superentity "It" renders the human civilization redundant and obsolete, Lymphater destroys "It". "It" already knew Lymphater's intentions, but was not worried, knowing that sooner or later someone else will create "It" again and again. "It" was only the first variant of Lymphater's formula and the second variant is possible. Lyphater wonders whether the second one would be capable to create the third stage of the evolution which would amount to an artificial God. == Publication history == It was translated in Russian (as "Формула Лимфатера") in 1963, in Hungarian (as "Lymphater utolsó képlete") in 1966, and in Bulgarian (as "Формулата на Лимфатер" by Георги Димитров Георгиев) in 1969. In 1973 an audiobook was released in German (as "Die lymphatersche Formel"), narrated by Martin Held. It was also republished (and translated) in some other collections of Lem's short stories.
Confidential computing
Confidential computing is a security and privacy-enhancing computational technique focused on protecting data in use. Confidential computing can be used in conjunction with storage and network encryption, which protect data at rest and data in transit respectively. It is designed to address software, protocol, cryptographic, and basic physical and supply-chain attacks, although some critics have demonstrated architectural and side-channel attacks effective against the technology. The technology protects data in use by performing computations in a hardware-based trusted execution environment (TEE). Confidential data is released to the TEE only once it is assessed to be trustworthy. Different types of confidential computing define the level of data isolation used, whether virtual machine, application, or function, and the technology can be deployed in on-premise data centers, edge locations, or the public cloud. It is often compared with other privacy-enhancing computational techniques such as fully homomorphic encryption, secure multi-party computation, and Trusted Computing. Confidential computing is promoted by the Confidential Computing Consortium (CCC) industry group, whose membership includes major providers of the technology. == Properties == Trusted execution environments (TEEs) "prevent unauthorized access or modification of applications and data while they are in use, thereby increasing the security level of organizations that manage sensitive and regulated data". Trusted execution environments can be instantiated on a computer's processing components such as a central processing unit (CPU) or a graphics processing unit (GPU). In their various implementations, TEEs can provide different levels of isolation including virtual machine, individual application, or compute functions. Typically, data in use in a computer's compute components and memory exists in a decrypted state and can be vulnerable to examination or tampering by unauthorized software or administrators. According to the CCC, confidential computing protects data in use through a minimum of three properties: Data confidentiality: "Unauthorized entities cannot view data while it is in use within the TEE". Data integrity: "Unauthorized entities cannot add, remove, or alter data while it is in use within the TEE". Code integrity: "Unauthorized entities cannot add, remove, or alter code executing in the TEE". In addition to trusted execution environments, remote cryptographic attestation is an essential part of confidential computing. The attestation process assesses the trustworthiness of a system and helps ensure that confidential data is released to a TEE only after it presents verifiable evidence that it is genuine and operating with an acceptable security posture. It allows the verifying party to assess the trustworthiness of a confidential computing environment through an "authentic, accurate, and timely report about the software and data state" of that environment. "Hardware-based attestation schemes rely on a trusted hardware component and associated firmware to execute attestation routines in a secure environment". Without attestation, a compromised system could deceive others into trusting it, claim it is running certain software in a TEE, and potentially compromise the confidentiality or integrity of the data being processed or the integrity of the trusted code. == Technical approaches == Technical approaches to confidential computing may vary in which software, infrastructure and administrator elements are allowed to access confidential data. The "trust boundary," which circumscribes a trusted computing base (TCB), defines which elements have the potential to access confidential data, whether they are acting benignly or maliciously. Confidential computing implementations enforce the defined trust boundary at a specific level of data isolation. The three main types of confidential computing are: Virtual machine isolation Application isolation, also known as process isolation Function isolation, also known as library isolation Virtual machine isolation removes the elements controlled by the computer infrastructure or cloud provider, but allows potential data access by elements inside a virtual machine running on the infrastructure. Application or process isolation permits data access only by authorized software applications or processes. Function or library isolation is designed to permit data access only by authorized subroutines or modules within a larger application, blocking access by any other system element, including unauthorized code in the larger application. == Threat model == As confidential computing is concerned with the protection of data in use, only certain threat models can be addressed by this technique. Other types of attacks are better addressed by other privacy-enhancing technologies. === In scope === The following threat vectors are generally considered in scope for confidential computing: Software attacks: including attacks on the host’s software and firmware. This may include the operating system, hypervisor, BIOS, other software and workloads. Protocol attacks: including "attacks on protocols associated with attestation as well as workload and data transport". This includes vulnerabilities in the "provisioning or placement of the workload" or data that could cause a compromise. Cryptographic attacks: including "vulnerabilities found in ciphers and algorithms due to a number of factors, including mathematical breakthroughs, availability of computing power and new computing approaches such as quantum computing". The CCC notes several caveats in this threat vector, including relative difficulty of upgrading cryptographic algorithms in hardware and recommendations that software and firmware be kept up-to-date. A multi-faceted, defense-in-depth strategy is recommended as a best practice. Basic physical attacks: including cold boot attacks, bus and cache snooping and plugging attack devices into an existing port, such as a PCI Express slot or USB port. Basic upstream supply-chain attacks: including attacks that would compromise TEEs through changes such as added debugging ports. The degree and mechanism of protection against these threats varies with specific confidential computing implementations. === Out of scope === Threats generally defined as out of scope for confidential computing include: Sophisticated physical attacks: including physical attacks that "require long-term and/or invasive access to hardware" such as chip scraping techniques and electron microscope probes. Upstream hardware supply-chain attacks: including attacks on the CPU manufacturing process, CPU supply chain in key injection/generation during manufacture. Attacks on components of a host system that are not directly providing the capabilities of the trusted execution environment are also generally out-of-scope. Availability attacks: confidential computing is designed to protect the confidentiality and integrity of protected data and code. It does not address availability attacks such as Denial of Service or Distributed Denial of Service attacks. == Use cases == Confidential computing can be deployed in the public cloud, on-premise data centers, or distributed "edge" locations, including network nodes, branch offices, industrial systems and others. === Data privacy and security === Confidential computing protects the confidentiality and integrity of data and code from the infrastructure provider, unauthorized or malicious software and system administrators, and other cloud tenants, which may be a concern for organizations seeking control over sensitive or regulated data. The additional security capabilities offered by confidential computing can help accelerate the transition of more sensitive workloads to the cloud or edge locations. === Multi-party analytics === Confidential computing can enable multiple parties to engage in joint analysis using confidential or regulated data inside a TEE while preserving privacy and regulatory compliance. In this case, all parties benefit from the shared analysis, but no party's sensitive data or confidential code is exposed to the other parties or system host. Examples include multiple healthcare organizations contributing data to medical research, or multiple banks collaborating to identify financial fraud or money laundering. Oxford University researchers proposed the alternative paradigm called "Confidential Remote Computing" (CRC), which supports confidential operations in Trusted Execution Environments across endpoint computers considering multiple stakeholders as mutually distrustful data, algorithm and hardware providers. === Confidential generative AI === Confidential computing technologies can be applied to various stages of a generative AI deployments to help increase data or model privacy, security, and regulatory compliance. TEEs and remote attestation can protect the integrity of data during AI model training, keep
Vague set
In mathematics, vague sets are an extension of fuzzy sets. In a fuzzy set, each object is assigned a single value in the interval [0,1] reflecting its grade of membership. This single value does not allow a separation of evidence for membership and evidence against membership. Gau et al. proposed the notion of vague sets, where each object is characterized by two different membership functions: a true membership function and a false membership function. This kind of reasoning is also called interval membership, as opposed to point membership in the context of fuzzy sets. == Mathematical definition == A vague set V {\displaystyle V} is characterized by its true membership function t v ( x ) {\displaystyle t_{v}(x)} its false membership function f v ( x ) {\displaystyle f_{v}(x)} with 0 ≤ t v ( x ) + f v ( x ) ≤ 1 {\displaystyle 0\leq t_{v}(x)+f_{v}(x)\leq 1} The grade of membership for x is not a crisp value anymore, but can be located in [ t v ( x ) , 1 − f v ( x ) ] {\displaystyle [t_{v}(x),1-f_{v}(x)]} . This interval can be interpreted as an extension to the fuzzy membership function. The vague set degenerates to a fuzzy set, if 1 − f v ( x ) = t v ( x ) {\displaystyle 1-f_{v}(x)=t_{v}(x)} for all x. The uncertainty of x is the difference between the upper and lower bounds of the membership interval; it can be computed as ( 1 − f v ( x ) ) − t v ( x ) {\displaystyle (1-f_{v}(x))-t_{v}(x)} .