Related papers: Chiron: A Set Theory with Types, Undefinedness, Qu…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
We describe an algorithm, meant to be very general, to compute a presentation of the group of units of an order in a (semi)simple algebra over Q. Our method is based on a generalisation of Vorono\"i's algorithm for computing perfect forms,…
We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…
A {\it dynamic reasoning system} (DRS) is an adaptation of a conventional formal logical system that explicitly portrays reasoning as a temporal activity, with each extralogical input to the system and each inference rule application being…
This paper describes a general framework for automatic termination analysis of logic programs, where we understand by ``termination'' the finitenes s of the LD-tree constructed for the program and a given query. A general property of…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
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…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
The basic ideas and power counting rules of chiral perturbation theory are discussed. The formalism of velocity dependent fields for baryons, and for hadrons containing a heavy quark, is explained. (Invited Talk, 1993 QCD Rencontres de…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
We analyze the structure of the group of (local) non-linear canonical transformations that exist in a system with n fermionic modes. To perform our study we develop an alternative framework to represent the generators of these canonical…
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
We describe a simple model that automatically generates the sum over gauge group representations and chiralities of a single generation of fermions in the Standard Model, augmented by a sterile neutrino. The model is a modification of the…
Inclusion logic is a variant of dependence logic that was shown to have the same expressive power as positive greatest fixed-point logic. Inclusion logic is not axiomatizable in full, but its first-order consequences can be axiomatized. In…
Compositional generalization is one of the main properties which differentiates lexical learning in humans from state-of-art neural networks. We propose a general framework for building models that can generalize compositionally using the…
Critical systems require high reliability and are present in many domains. They are systems in which failure may result in financial damage or even loss of lives. Standard techniques of software engineering are not enough to ensure the…
First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…
We reexamine critically the chiral expansion for the baryon magnetic moments including the contributions from loops which involve intermediate octet and decuplet baryons. We find that, contrary to some claims, the nonanalytic loop…
We propose an abstract notion of a type theory to unify the semantics of various type theories including Martin-L\"{o}f type theory, two-level type theory and cubical type theory. We establish basic results in the semantics of type theory:…