Related papers: A Fuzzy Syllogistic Reasoning Schema for Generaliz…
This article contains ideas and their elaboration for quantifiers, which appeared after checking in practice the experimental language of the formal knowledge representation YAFOLL [1]: - looking at for_all and exists quantifiers as…
A new understanding of the notion of regularizer is proposed. It is argued that this new notion is more realistic than the old one and better fits the practical computational needs. An example of the regularizer in the new sense is given. A…
Large language models (LLMs) have a substantial capacity for high-level analogical reasoning: reproducing patterns in linear text that occur in their training data (zero-shot evaluation) or in the provided context (few-shot in-context…
A notion of generalized quantifier in computational complexity theory is explored and used to give a unified treatment of leaf language definability, oracle separations, type 2 operators, and circuits with monoidal gates. Relations to…
Generalized quantifiers (e.g., few, most) are used to indicate the proportions predicates are satisfied (for example, some apples are red). One way to interpret quantifier semantics is to explicitly bind these satisfactions with percentage…
Qualitative relationships illustrate how changing one property (e.g., moving velocity) affects another (e.g., kinetic energy) and constitutes a considerable portion of textual knowledge. Current approaches use either semantic parsers to…
People can refer to quantities in a visual scene by using either exact cardinals (e.g. one, two, three) or natural language quantifiers (e.g. few, most, all). In humans, these two processes underlie fairly different cognitive and neural…
We present a logical framework to represent and reason about fuzzy optimization problems based on fuzzy answer set optimization programming. This is accomplished by allowing fuzzy optimization aggregates, e.g., minimum and maximum in the…
Large language models (LLMs) excel at complex tasks with advances in reasoning capabilities. However, existing reward mechanisms remain tightly coupled to final correctness and pay little attention to the underlying reasoning process:…
When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to an arbitrary set of axioms is hard, even for relatively…
The rules of canonical quantization normally offer good results, but sometimes they fail, e.g., leading to quantum triviality ($=$ free) for certain examples that are classically nontrivial ($\ne$ free). A new procedure, called Enhanced…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking…
In various applications the search for certificates for certain properties (e.g., stability of dynamical systems, program termination) can be formulated as a quantified constraint solving problem with quantifier prefix exists-forall. In…
As deep neural models in NLP become more complex, and as a consequence opaque, the necessity to interpret them becomes greater. A burgeoning interest has emerged in rationalizing explanations to provide short and coherent justifications for…
Sequence models are a critical component of modern NLP systems, but their predictions are difficult to explain. We consider model explanations though rationales, subsets of context that can explain individual model predictions. We find…
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. In this paper, first we state and prove a…
This paper proposes a way to compute the meanings associated with sentences with generic noun phrases corresponding to the generalized quantifier most. We call these generics specimens and they resemble stereotypes or prototypes in lexical…
Quantified constraints and Quantified Boolean Formulae are typically much more difficult to reason with than classical constraints, because quantifier alternation makes the usual notion of solution inappropriate. As a consequence, basic…
Linear representations for a subclass of boolean symmetric functions selected by a parity condition are shown to constitute a generalization of the linear constraints on probabilities introduced by Boole. These linear constraints are…