Related papers: Adequate and computational encodings in the logica…
Decoding of convolutional codes poses a significant challenge for coding theory. Classical methods, based on e.g. Viterbi decoding, suffer from being computationally expensive and are restricted therefore to codes of small complexity. Based…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
The work concerns automatic generation of logical specifications from requirements models. Logical specifications obtained in such a way can be subjected to formal verification using deductive reasoning. Formal verification concerns…
Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in English natural language. While the progress is promising, it is currently unclear if these models…
While linear programming (LP) decoding provides more flexibility for finite-length performance analysis than iterative message-passing (IMP) decoding, it is computationally more complex to implement in its original form, due to both the…
Although LLMs have shown great performance on Mathematics and Coding related reasoning tasks, the reasoning capabilities of LLMs regarding other forms of reasoning are still an open problem. Here, we examine the issue of reasoning from the…
Computationally intensive decoding procedures--including search, reranking, and self-critique--can improve the quality of language model (LM) outputs in problems spanning code generation, numerical reasoning, and dialog. Existing work…
Behind a set of rules in Deontic Defeasible Logic, there is a mapping process of normative background fragments. This process goes from text to rules and implicitly encompasses an explanation of the coded fragments. In this paper we deliver…
Reasoning encompasses two typical types: deductive reasoning and inductive reasoning. Despite extensive research into the reasoning capabilities of Large Language Models (LLMs), most studies have failed to rigorously differentiate between…
Large language models (LLMs) are increasingly used in situations where human values are at stake, such as decision-making tasks that involve reasoning when performed by humans. We investigate the so-called reasoning capabilities of LLMs…
In context learning (ICL) underpins recent advances in large language models (LLMs), although its role and performance in causal reasoning remains unclear. Causal reasoning demands multihop composition and strict conjunctive control, and…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
As fault-tolerant quantum computers scale, certifying the accuracy of computations performed with encoded logical qubits will soon become classically intractable. This creates a critical need for scalable, device-independent certification…
In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof…
Applying machine learning to mathematical terms and formulas requires a suitable representation of formulas that is adequate for AI methods. In this paper, we develop an encoding that allows for logical properties to be preserved and is…
Logical operations are essential for quantum computation within quantum error-correcting codes. However, discovering their physical realizations is challenging, especially for non-additive codes that lack a stabilizer description. We…
In this work, we present hardware and software implementations of flexible polar systematic encoders and decoders. The proposed implementations operate on polar codes of any length less than a maximum and of any rate. We describe the…
The benchmark for computation is typically given as Turing computability; the ability for a computation to be performed by a Turing Machine. Many languages exploit (indirect) encodings of Turing Machines to demonstrate their ability to…
We present a system called Adelfa that provides mechanized support for reasoning about specifications developed in the Edinburgh Logical Framework or LF. Underlying Adelfa is a new logic named L_LF. Typing judgements in LF are represented…
Masked diffusion language models (MDLMs) are trained to in-fill positions in randomly masked sequences, in contrast to next-token prediction models. Discussions around MDLMs focus on two benefits: (1) any-order decoding and 2) multi-token…