Simplification of many-valued logic formulas using anti-links

We present the theoretical foundations of the many-valued generalization of a technique for simplifying large non-clausal formulas in propositional logic, that is called "removal of anti-links". Possible applications of anti-links include computation of prime implicates of large non-clausal formulas as required, for example, in diagnosis. Anti-links do not compute any normal form of a given formula themselves, rather, they remove certain forms of redundancy from formulas in negation normal form (NNF). Their main advantage is that no clausal normal form has to be computed in order to remove redundant parts of a formula. In this paper, we define an anti-link operation on a generic language for expressing many-valued logic formulas called "signed NNF" and we show that all interesting properties of two-valued anti-links generalize to the many-valued setting, although in a non-trivial way

What do Topologists want from Seiberg--Witten theory? (A review of four-dimensional topology for physicists)

In 1983, Donaldson shocked the topology world by using instantons from physics to prove new theorems about four-dimensional manifolds, and he developed new topological invariants. In 1988, Witten showed how these invariants could be obtained by correlation functions for a twisted N=2 SUSY gauge theory. In 1994, Seiberg and Witten discovered dualities for such theories, and in particular, developed a new way of looking at four-dimensional manifolds that turns out to be easier, and is conjectured to be equivalent to, Donaldson theory. This review describes the development of this mathematical subject, and shows how the physics played a pivotal role in the current understanding of this area of topology.Comment: 51 pages, 10 figures, 8 postscript files. Submitted to International Journal of Modern Physics A, July 2002 Uses Latex 2e with class file ws-ijmpa.cls (included in tar file

Conditionals and modularity in general logics

In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics

On skew tau-functions in higher spin theory

Recent studies of higher spin theory in three dimensions concentrate on Wilson loops in Chern-Simons theory, which in the classical limit reduce to peculiar corner matrix elements between the highest and lowest weight states in a given representation of SL(N). Despite these "skew" tau-functions can seem very different from conventional ones, which are the matrix elements between the two highest weight states, they also satisfy the Toda recursion between different fundamental representations. Moreover, in the most popular examples they possess simple representations in terms of matrix models and Schur functions. We provide a brief introduction to this new interesting field, which, after quantization, can serve as an additional bridge between knot and integrability theories.Comment: 36 page

The geometry of variations in Batalin-Vilkovisky formalism

This is a paper about geometry of (iterated) variations. We explain why no sources of divergence are built into the Batalin-Vilkovisky (BV) Laplacian, whence there is no need to postulate any ad hoc conventions such as "$\delta(0)=0$" and "$\log\delta(0)=0$" within BV-approach to quantisation of gauge systems. Remarkably, the geometry of iterated variations does not refer at all to the construction of Dirac's $\delta$-function as a limit of smooth kernels. We illustrate the reasoning by re-deriving - but not just "formally postulating" - the standard properties of BV-Laplacian and Schouten bracket and by verifying their basic inter-relations (e.g., cohomology preservation by gauge symmetries of the quantum master-equation).Comment: XXI International Conference on Integrable Systems and Quantum Symmetries (ISQS21) 11-16 June 2013 at CVUT Prague, Czech Republic; 51 pages (9 figures). - Main Example 2.4 on pp.34-36 retained from arXiv:1302.4388v1, standard proofs in Appendix A amended and quoted from arXiv:1302.4388v1 (joint with S.Ringers). - Solution to Exercise 11.6 from IHES/M/12/13 by the same autho

Enterprise model verification and validation : an approach

This article presents a verification and validation approach which is used here in order to complete the classical tool box the industrial user may utilize in enterprise modeling and integration domain. This approach, which has been defined independently from any application domain is based on several formal concepts and tools presented in this paper. These concepts are property concepts, property reference matrix, properties graphs, enterprise modeling domain ontology, conceptual graphs and formal reasoning mechanisms

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book