Annals of Mathematics and Artificial Intelligence最新文献

{"title":"A faster implementation of EQ and SE queries for switch-list representations","authors":"Ondřej Čepek,&nbsp;James Weigle","doi":"10.1007/s10472-023-09915-5","DOIUrl":"10.1007/s10472-023-09915-5","url":null,"abstract":"<div><p>A switch-list representation (SLR) of a Boolean function is a compressed truth table representation of a Boolean function in which only (i) the function value of the first row in the truth table and (ii) a list of switches are stored. A switch is a Boolean vector whose function value differs from the value of the preceding Boolean vector in the truth table. The paper Čepek and Chromý (JAIR 2020) systematically studies the properties of SLRs and among other results gives polynomial-time algorithms for all standard queries investigated in the Knowledge Compilation Map introduced in Darwiche and Marquis (JAIR 2002). These queries include consistency check, validity check, clausal entailment check, implicant check, equivalence check, sentential entailment check, model counting, and model enumeration. The most difficult query supported in polynomial time by the smallest number of representation languages considered in the Knowledge Compilation Map is the sentential entailment check (of which the equivalence check is a special case). This query can be answered in polynomial time for SLRs, as shown in Čepek and Chromý (JAIR 2020). However, the query-answering algorithm is an indirect one: it first compiles both input SLRs into OBDDs (changing the order of variables for one of them if necessary) and then runs the sentential entailment check on the constructed OBDDs (both respecting the same order of variables) using an algorithm from the monograph by Wegener (2000). In this paper we present algorithms that answer both the equivalence and the sentential entailment query directly by manipulating the input SLRs (hence eliminating the compilation step into OBDD), which in both cases improves the time complexity of answering the query by a factor of <i>n</i> for input SLRs on <i>n</i> variables.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 5","pages":"1097 - 1112"},"PeriodicalIF":1.2,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138680596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An abstract view on optimizations in propositional frameworks","authors":"Yuliya Lierler","doi":"10.1007/s10472-023-09914-6","DOIUrl":"10.1007/s10472-023-09914-6","url":null,"abstract":"<div><p>Search/optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared toward solving and modeling search/optimization problems. Automated reasoning and knowledge representation are the subfields of AI that are particularly vested in these developments. Many popular automated reasoning paradigms provide users with languages supporting optimization statements: answer set programming or MaxSAT or <span>min-one</span>, to name a few. These paradigms vary significantly in their languages and in the ways they express quality conditions on computed solutions. Here we propose a unifying framework of so-called weight systems that eliminates syntactic distinctions between paradigms and allows us to see essential similarities and differences between optimization statements provided by paradigms. This unifying outlook has significant simplifying and explanatory potential in the studies of optimization and modularity in automated reasoning and knowledge representation. It also supplies researchers with a convenient tool for proving the formal properties of distinct frameworks; bridging these frameworks; and facilitating the development of translational solvers.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 2","pages":"355 - 391"},"PeriodicalIF":1.2,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138680461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Collective combinatorial optimisation as judgment aggregation","authors":"Linus Boes,&nbsp;Rachael Colley,&nbsp;Umberto Grandi,&nbsp;Jérôme Lang,&nbsp;Arianna Novaro","doi":"10.1007/s10472-023-09910-w","DOIUrl":"10.1007/s10472-023-09910-w","url":null,"abstract":"<div><p>In many settings, a collective decision has to be made over a set of alternatives that has a combinatorial structure: important examples are multi-winner elections, participatory budgeting, collective scheduling, and collective network design. A further common point of these settings is that agents generally submit preferences over issues (e.g., projects to be funded), each having a cost, and the goal is to find a feasible solution maximising the agents’ satisfaction under problem-specific constraints. We propose the use of judgment aggregation as a unifying framework to model these situations, which we refer to as collective combinatorial optimisation problems. Despite their shared underlying structure, collective combinatorial optimisation problems have so far been studied independently. Our formulation into judgment aggregation connects them, and we identify their shared structure via five case studies of well-known collective combinatorial optimisation problems, proving how popular rules independently defined for each problem actually coincide. We also chart the computational complexity gap that may arise when using a general judgment aggregation framework instead of a specific problem-dependent model.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 6","pages":"1437 - 1465"},"PeriodicalIF":1.2,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10472-023-09910-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138680597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence and verification of Nash equilibria in non-cooperative contribution games with resource contention","authors":"Nicolas Troquard","doi":"10.1007/s10472-023-09905-7","DOIUrl":"10.1007/s10472-023-09905-7","url":null,"abstract":"<div><p>In resource contribution games, a class of non-cooperative games, the players want to obtain a bundle of resources and are endowed with bags of bundles of resources that they can make available into a common for all to enjoy. Available resources can then be used towards their private goals. A player is potentially satisfied with a profile of contributed resources when his bundle could be extracted from the contributed resources. Resource contention occurs when the players who are potentially satisfied, cannot actually all obtain their bundle. The player’s preferences are always single-minded (they consider a profile good or they do not) and parsimonious (between two profiles that are equally good, they prefer the profile where they contribute less). What makes a profile of contributed resources good for a player depends on their attitude towards resource contention. We study the problem of deciding whether an outcome is a pure Nash equilibrium for three kinds of players’ attitudes towards resource contention: public contention-aversity, private contention-aversity, and contention-tolerance. In particular, we demonstrate that in the general case when the players are contention-averse, then the problem is harder than when they are contention-tolerant. We then identify a natural class of games where, in presence of contention-averse preferences, it becomes tractable, and where there is always a Nash equilibrium.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 2","pages":"317 - 353"},"PeriodicalIF":1.2,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10472-023-09905-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139002028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Theory and algorithms for learning with rejection in binary classification","authors":"Corinna Cortes,&nbsp;Giulia DeSalvo,&nbsp;Mehryar Mohri","doi":"10.1007/s10472-023-09899-2","DOIUrl":"10.1007/s10472-023-09899-2","url":null,"abstract":"<div><p>We introduce a novel framework for classification with a rejection option that consists of simultaneously learning two functions: a classifier along with a rejection function. We present a full theoretical analysis of this framework including new data-dependent learning bounds in terms of the Rademacher complexities of the classifier and rejection families as well as consistency and calibration results. These theoretical guarantees guide us in designing new algorithms that can exploit different kernel-based hypothesis sets for the classifier and rejection functions. We compare our general framework with the special case of confidence-based rejection for which we also devise alternative loss functions and algorithms. We report the results of several experiments showing that our kernel-based algorithms can yield a notable improvement over the best existing confidence-based rejection algorithm.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 2","pages":"277 - 315"},"PeriodicalIF":1.2,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139005903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Logic program proportions","authors":"Christian Antić","doi":"10.1007/s10472-023-09904-8","DOIUrl":"https://doi.org/10.1007/s10472-023-09904-8","url":null,"abstract":"<p>The purpose of this paper is to present a fresh idea on how symbolic learning might be realized via analogical reasoning. For this, we introduce directed analogical proportions between logic programs of the form “<i>P</i> transforms into <i>Q</i> as <i>R</i> transforms into <i>S</i>” as a mechanism for deriving similar programs by analogy-making. The idea is to instantiate a fragment of a recently introduced abstract algebraic framework of analogical proportions in the domain of logic programming. Technically, we define proportions in terms of modularity where we derive abstract forms of concrete programs from a “known” source domain which can then be instantiated in an “unknown” target domain to obtain analogous programs. To this end, we introduce algebraic operations for syntactic logic program composition and concatenation. Interestingly, our work suggests a close relationship between modularity, generalization, and analogy which we believe should be explored further in the future. In a broader sense, this paper is a further step towards a mathematical theory of logic-based analogical reasoning and learning with potential applications to open AI-problems like commonsense reasoning and computational learning and creativity.</p>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"24 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tractable representations for Boolean functional synthesis","authors":"S. Akshay,&nbsp;Supratik Chakraborty,&nbsp;Shetal Shah","doi":"10.1007/s10472-023-09907-5","DOIUrl":"10.1007/s10472-023-09907-5","url":null,"abstract":"<div><p>Given a Boolean relational specification <span>(F(textbf{X}, textbf{Y}))</span>, where <span>(textbf{X})</span> is a vector of inputs and <span>(textbf{Y})</span> is a vector of outputs, Boolean functional synthesis requires us to compute a vector of (Skolem) functions <span>(varvec{Psi }(textbf{X}))</span>, one for each output in <span>(textbf{Y})</span>, such that <span>(F(textbf{X}, varvec{Psi }(textbf{X})) leftrightarrow exists textbf{Y},F(textbf{X},textbf{Y}))</span> holds. This problem lies at the heart of many applications and has received significant attention in recent years. In this paper, we investigate the role of representation of <span>(F(textbf{X}, textbf{Y}))</span> and of <span>(varvec{Psi }(textbf{X}))</span> in determining the computational hardness of Boolean functional synthesis. We start by showing that an efficient way of existentially quantifying variables from a Boolean formula in a given order yields an efficient solution to Boolean functional synthesis and vice versa. We then propose a semantic normal form, called <span>SynNNF</span>, that guarantees polynomial-time synthesis and characterizes polynomial-time existential quantification for a given order of quantification of variables. We show that several syntactic and other semantic normal forms for Boolean formulas studied in the knowledge compilation literature are subsumed by <span>SynNNF</span>, and that <span>SynNNF</span> is exponentially more succinct than most of them. We also investigate how the representation of the synthesized (Skolem) functions <span>(varvec{Psi }(textbf{X}))</span> affects the complexity of Boolean functional synthesis, and present a map of complexity based on the representations of <span>(F(textbf{X},textbf{Y}))</span> and <span>(varvec{Psi }(textbf{X}))</span>. Finally, we propose an algorithm to compile a specification represented as a <span>NNF</span> (including <span>CNF</span>) circuit to <span>SynNNF</span>. We present results of an extensive set of experiments conducted using an implementation of the above algorithm, and two other tools available in the public domain.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 5","pages":"1051 - 1096"},"PeriodicalIF":1.2,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An improvement of Random Node Generator for the uniform generation of capacities","authors":"Peiqi Sun,&nbsp;Michel Grabisch,&nbsp;Christophe Labreuche","doi":"10.1007/s10472-023-09911-9","DOIUrl":"10.1007/s10472-023-09911-9","url":null,"abstract":"<div><p>Capacity is an important tool in decision-making under risk and uncertainty and multi-criteria decision-making. When learning a capacity-based model, it is important to be able to generate uniformly a capacity. Due to the monotonicity constraints of a capacity, this task reveals to be very difficult. The classical Random Node Generator (RNG) algorithm is a fast-running speed capacity generator, however with poor performance. In this paper, we firstly present an exact algorithm for generating a <i>n</i> elements’ general capacity, usable when <span>(n &lt; 5)</span>. Then, we present an improvement of the classical RNG by studying the distribution of the value of each element of a capacity. Furthermore, we divide it into two cases, the first one is the case without any conditions, and the second one is the case when some elements have been generated. Experimental results show that the performance of this improved algorithm is much better than the classical RNG while keeping a very reasonable computation time.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 6","pages":"1381 - 1406"},"PeriodicalIF":1.2,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling and shadowing paraconsistent BDI agents","authors":"Barbara Dunin-Kęplicz,&nbsp;Andrzej Szałas","doi":"10.1007/s10472-023-09902-w","DOIUrl":"10.1007/s10472-023-09902-w","url":null,"abstract":"<div><p>The <span>Bdi</span> model of rational agency has been studied for over three decades. Many robust multiagent systems have been developed, and a number of <span>Bdi</span> logics have been studied. Following this intensive development phase, the importance of integrating <span>Bdi</span> models with inconsistency handling and revision theory have been emphasized. There is also a demand for a tighter connection between <span>Bdi</span>-based implementations and <span>Bdi</span> logics. In this paper, we address these postulates by introducing a novel, paraconsistent logical <span>Bdi</span> model close to implementation, with building blocks that can be represented as <span>Sql</span>/rule-based databases. Importantly, tractability is achieved by reasoning as querying. This stands in a sharp contrast to the high complexity of known <span>Bdi</span> logics. We also extend belief shadowing, a shallow and lightweight alternative to deep and computationally demanding belief revision, to encompass agents’ motivational attitudes.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 4","pages":"855 - 876"},"PeriodicalIF":1.2,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10472-023-09902-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Socially conscious stability for tiered coalition formation games","authors":"Nathan Arnold,&nbsp;Sarah Snider,&nbsp;Judy Goldsmith","doi":"10.1007/s10472-023-09897-4","DOIUrl":"10.1007/s10472-023-09897-4","url":null,"abstract":"<div><p>We investigate Tiered Coalition Formation Games (TCFGs), a cooperative game inspired by the stratification of Pokémon on the fan website, Smogon. It is known that, under match-up oriented preferences, Nash and core stability are equivalent. We previously introduced a notion of <i>socially conscious stability</i> for TCFGs, and introduced a game variant with fixed <i>k</i>-length tier lists. In this work we show that in tier lists under match-up oriented preferences, socially conscious stability is equivalent to Nash stability and to core stability, but in <i>k</i>-tier lists, the three stability notions are distinct. We also give a necessary condition for tier list stability in terms of robustness (the minimum in-tier utility of an agent). We introduce a notion of approximate Nash stability and approximately socially conscious stability, and provide experiments on the empirical run time of our <i>k</i>-tier local search algorithm, and the performance of our algorithms for generating approximately socially consciously stable tier lists.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 3","pages":"539 - 580"},"PeriodicalIF":1.2,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}