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Decision theory has become widely accepted in the AI community as a useful framework for planning and decision making. Applying the framework typically requires elicitation of some form of probability and utility information. While much…
The Lov\'{a}sz Local Lemma is a central tool in probabilistic combinatorics, providing a sufficient condition under which a finite collection of undesirable events with limited dependencies can be simultaneously avoided with positive…
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…
The "correct by construction" paradigm is an important component of modern Formal Methods, and here we use the probabilistic Guarded-Command Language $\mathit{pGCL}$ to illustrate its application to $\mathit{probabilistic}$ programming.…
There is a well-known equivalence between avoiding accuracy dominance and having probabilistically coherent credences (see, e.g., de Finetti 1974, Joyce 2009, Predd et al. 2009, Schervish et al. 2009, Pettigrew 2016). However, this…
Recent advances in reasoning with large language models (LLMs) have demonstrated strong performance on complex mathematical tasks, including combinatorial optimization. Techniques such as Chain-of-Thought and In-Context Learning have…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
This work is based on the idea that extension of physical and mathematical theories to include the amount of space, time, momentum, and energy resources required to determine properties of systems may influence what is true in physics and…
This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…
We introduce the Dichotomy Property, a new property of some languages in Set Computable Theory, in order to explore the expressivity of some languages which are extensions of MLS. By-product we prove undecidability of MLS extended with not…
In this paper, a Gaifman-Shapiro-style module architecture is tailored to the case of Smodels programs under the stable model semantics. The composition of Smodels program modules is suitably limited by module conditions which ensure the…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
This paper provides a model theoretic semantics to feature terms augmented with set descriptions. We provide constraints to specify HPSG style set descriptions, fixed cardinality set descriptions, set-membership constraints, restricted…
This paper concerns the development of metatheory for extensible languages. It uses as its starting point a view that programming languages tailored to specific application domains are to be constructed by composing components from an open…
Conditional specification of distributions is a developing area with many applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we propose an alternative approach to study the…