Related papers: Encoding Arguments
Proofs (sequent calculus, natural deduction) and imperative algorithms (pseudocodes) are two well-known coexisting concepts. Then what is their relationship? Our answer is that \[ imperative\ algorithms\ =\ proofs\ with\ cuts \] This…
While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…
We encode/decode Prolog terms as unique natural numbers. Our encodings have the following properties: a) are bijective b) natural numbers always decode to syntactically valid terms c) they work in low polynomial time in the bitsize of the…
A framework is presented for a computational theory of probabilistic argument. The Probabilistic Reasoning Environment encodes knowledge at three levels. At the deepest level are a set of schemata encoding the system's domain knowledge.…
The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In most approaches, the system is considered a black box, making it difficult to generate…
Large language models (LLMs) often benefit from intermediate steps of reasoning to generate answers to complex problems. When these intermediate steps of reasoning are used to monitor the activity of the model, it is essential that this…
We consider Proof Complexity in light of the unusual binary encoding of certain combinatorial principles. We contrast this Proof Complexity with the normal unary encoding in several refutation systems, based on Resolution and Integer Linear…
Understanding the behavior of learned classifiers is an important task, and various black-box explanations, logical reasoning approaches, and model-specific methods have been proposed. In this paper, we introduce probabilistic sufficient…
A central question for knowledge representation is how to encode and handle uncertain knowledge adequately. We introduce the probabilistic description logic ALCP that is designed for representing context-dependent knowledge, where the…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…
Prediction without justification has limited applicability. As a remedy, we learn to extract pieces of input text as justifications -- rationales -- that are tailored to be short and coherent, yet sufficient for making the same prediction.…
We introduce \emph{Term Coding}, a novel framework for analysing extremal problems in discrete mathematics by encoding them as finite systems of \emph{term equations} (and, optionally, \emph{non-equality constraints}). In its basic form,…
The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic…
In this paper will be presented methodology of encoding information in valuations of discrete lattice with some translational invariant constrains in asymptotically optimal way. The method is based on finding statistical description of such…
Argumentation is the process of constructing arguments about propositions, and the assignment of statements of confidence to those propositions based on the nature and relative strength of their supporting arguments. The process is modelled…
We consider the problem of intruder deduction in security protocol analysis: that is, deciding whether a given message $M$ can be deduced from a set of messages $\Gamma$ under the theory of blind signatures and arbitrary convergent…
The DNA storage channel is considered, in which a codeword is comprised of $M$ unordered DNA molecules. At reading time, $N$ molecules are sampled with replacement, and then each molecule is sequenced. A coded-index concatenated-coding…
A central topic in mathematical logic is the classification of theorems from mathematics in hierarchies according to their logical strength. Ideally, the place of a theorem in a hierarchy does not depend on the representation (aka coding)…
We encode arrays as functions which, in turn, are encoded as sets of ordered pairs. The set cardinality of each of these functions coincides with the length of the array it is representing. Then we define a fragment of set theory that is…