Related papers: Uniform Agent-interpolation of Distributed Knowled…
This paper introduces the concept of hyperpolation: a way of generalising from a limited set of data points that is a peer to the more familiar concepts of interpolation and extrapolation. Hyperpolation is the task of estimating the value…
The Uniform Information Density (UID) hypothesis posits that speakers tend to distribute information evenly across linguistic units to achieve efficient communication. Of course, information rate in texts and discourses is not perfectly…
We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and…
The usual power function error estimates do not capture the true order of uniform accuracy for thin plate spline interpolation to smooth data functions in one variable. In this paper we propose a new type of power function and we show,…
The Craig interpolation property (CIP) states that an interpolant for an implication exists iff it is valid. The projective Beth definability property (PBDP) states that an explicit definition exists iff a formula stating implicit…
We introduce an autonomous multiagent framework for mechanistic interpretability that automates both explaining and finding internal features in large language models. The system runs two coupled loops: (1) explanation refinement, where an…
The framework of algorithmic knowledge assumes that agents use algorithms to compute the facts they explicitly know. In many cases of interest, a deductive system, rather than a particular algorithm, captures the formal reasoning used by…
Although AI agents have demonstrated impressive capabilities in long-horizon reasoning, their reliability is severely hampered by the ``Spiral of Hallucination,'' where early epistemic errors propagate irreversibly. Existing methods face a…
A practical notation can convey valuable intuitions and concisely express new ideas. Information theory is of importance to machine learning, but the notation for information-theoretic quantities is sometimes opaque. We propose a practical…
We present a unified interpolation scheme that combines compactly-supported positive-definite kernels and multivariate polynomials. This unified framework generalizes interpolation with compactly-supported kernels and also classical…
Characterization of successful formulas in Public Announcement Logic (PAL) is a well known open problem in Dynamic Epistemic Logic. Recently, Holliday and ICard have given a complete characterization for the single agent case. However, the…
We consider the family of guarded and unguarded ordered logics, that constitute a recently rediscovered family of decidable fragments of first-order logic (FO), in which the order of quantification of variables coincides with the order in…
Epistemic logic is known as a logic that captures the knowledge and beliefs of agents and has undergone various developments since Hintikka (1962). In this paper, we propose a new logic called agent-knowledge logic by taking the product of…
In this paper we analyze the computational power of variants of population protocols (PP), a formalism for distributed systems with anonymous agents having very limited capabilities. The capabilities of agents are enhanced in mediated…
Information Pursuit (IP) is an explainable prediction algorithm that greedily selects a sequence of interpretable queries about the data in order of information gain, updating its posterior at each step based on observed query-answer pairs.…
Knowledge graphs (KGs) have become valuable knowledge resources in various applications, and knowledge graph embedding (KGE) methods have garnered increasing attention in recent years. However, conventional KGE methods still face challenges…
This paper presents evidence for the idea that much of artificial intelligence, human perception and cognition, mainstream computing, and mathematics, may be understood as compression of information via the matching and unification of…
We start a systematic investigation of the size of Craig interpolants, uniform interpolants, and strongest implicates for (quasi-)normal modal logics. Our main upper bound states that for tabular modal logics, the computation of strongest…
In logics with the Craig interpolation property (CIP) the existence of an interpolant for an implication follows from the validity of the implication. In logics with the projective Beth definability property (PBDP), the existence of an…
Deep learning has emerged as a versatile tool for a wide range of NLP tasks, due to its superior capacity in representation learning. But its applicability is limited by the reliance on annotated examples, which are difficult to produce at…