Related papers: On Successive Approximations To The Choice Problem…

Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…

We consider modeling the conception of knowledge in terms of temporal logic. The study of knowledge logical operations is originated around 1962 by representation of knowledge and belief using modalities. Nowadays, it is very good…

Although large language models demonstrate emergent abilities in solving math word problems, there is a challenging task in complex multi-step mathematical reasoning tasks. To improve model performance on mathematical reasoning tasks,…

We propose a society-first theory of normative appropriateness where individuals, modeled as pre-trained actors with cognitive architectures analogous to Large Language Models (LLMs), generate behavior via predictive pattern completion. Our…

In earlier work, we introduced the framework of language-based decisions, the core idea of which was to modify Savage's classical decision-theoretic framework by taking actions to be descriptions in some language, rather than functions from…

Human cognition is profoundly shaped by the environments in which it unfolds. Yet, it remains an open question whether learning and decision making can be explained as a principled adaptation to the statistical structure of real-world…

This work presents an operational and geometric approach to logic. It starts from the multilinear elective decomposition of binary logical functions in the original form introduced by George Boole. A justification on historical grounds is…

We conducted three experiments to investigate how large language models (LLMs) evaluate posterior probabilities. Our results reveal the coexistence of two modes in posterior judgment among state-of-the-art models: a normative mode, which…

We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…

We report on the mechanization of (preference-based) conditional normative reasoning. Our focus is on Aqvist's system E for conditional obligation, and its extensions. Our mechanization is achieved via a shallow semantical embedding in…

In this article, we employ mathematical concepts as a tool to examine the phenomenon of consciousness experience and logical phenomena. Through our investigation, we aim to demonstrate that our experiences, while not confined to…

At the core of our uniquely human cognitive abilities is the capacity to see things from different perspectives, or to place them in a new context. We propose that this was made possible by two cognitive transitions. First, the large brain…

Rational decision making in its linguistic description means making logical decisions. In essence, a rational agent optimally processes all relevant information to achieve its goal. Rationality has two elements and these are the use of…

Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis (1973) earlier considered such a notion of relative likelihood in the…

People acquire concepts through rich physical and social experiences and use them to understand and navigate the world. In contrast, large language models (LLMs), trained solely through next-token prediction on text, exhibit strikingly…

This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…

A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…

Human decision-making deviates from the optimal solution, that maximizes cumulative rewards, in many situations. Here we approach this discrepancy from the perspective of bounded rationality and our goal is to provide a justification for…

Achieving human-level intelligence requires refining the transition from the fast, intuitive System 1 to the slower, more deliberate System 2 reasoning. While System 1 excels in quick, heuristic decisions, System 2 relies on logical…

Recent advances in large language models (LLMs) have made reasoning a central benchmark for evaluating intelligence. While prior surveys focus on efficiency by examining how to shorten reasoning chains or reduce computation, this view…