Patrik AdriánUniversity of Debrecen, Faculty of Informatics, György VaszilUniversity of Debrecen, Faculty of Informatics
Boolean grammars generalize context-free rewriting by extending the possibilities when dealing with different rules for the same nonterminal symbol. By allowing not only disjunction (as in the case of usual context-free grammars), but also conjunction and negation as possible connections between different rules with the same left-hand side, they are able to simplify the description of context-free languages and characterize languages that are not context-free. The use of negation, however, leads to the possibility of introducing rules that interplay in such a way which is problematic to handle in the classical, two-valued logical setting. Here we define a three valued interpretation to deal with such contradictory grammars using a method introduced originally in the context of logic programming, and present an algorithm to determine the membership status of strings with respect to the resulting three valued languages.
{"title":"A GLR-like Parsing Algorithm for Three-Valued Interpretations of Boolean Grammars with Strong Negation","authors":"Patrik AdriánUniversity of Debrecen, Faculty of Informatics, György VaszilUniversity of Debrecen, Faculty of Informatics","doi":"arxiv-2409.06966","DOIUrl":"https://doi.org/arxiv-2409.06966","url":null,"abstract":"Boolean grammars generalize context-free rewriting by extending the\u0000possibilities when dealing with different rules for the same nonterminal\u0000symbol. By allowing not only disjunction (as in the case of usual context-free\u0000grammars), but also conjunction and negation as possible connections between\u0000different rules with the same left-hand side, they are able to simplify the\u0000description of context-free languages and characterize languages that are not\u0000context-free. The use of negation, however, leads to the possibility of\u0000introducing rules that interplay in such a way which is problematic to handle\u0000in the classical, two-valued logical setting. Here we define a three valued\u0000interpretation to deal with such contradictory grammars using a method\u0000introduced originally in the context of logic programming, and present an\u0000algorithm to determine the membership status of strings with respect to the\u0000resulting three valued languages.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider credibility-limited revision in the framework of belief change for epistemic spaces, permitting inconsistent belief sets and inconsistent beliefs. In this unrestricted setting, the class of credibility-limited revision operators does not include any AGM revision operators. We extend the class of credibility-limited revision operators in a way that all AGM revision operators are included while keeping the original spirit of credibility-limited revision. Extended credibility-limited revision operators are defined axiomatically. A semantic characterization of extended credibility-limited revision operators that employ total preorders on possible worlds is presented.
{"title":"Credibility-Limited Revision for Epistemic Spaces","authors":"Kai Sauerwald","doi":"arxiv-2409.07119","DOIUrl":"https://doi.org/arxiv-2409.07119","url":null,"abstract":"We consider credibility-limited revision in the framework of belief change\u0000for epistemic spaces, permitting inconsistent belief sets and inconsistent\u0000beliefs. In this unrestricted setting, the class of credibility-limited\u0000revision operators does not include any AGM revision operators. We extend the\u0000class of credibility-limited revision operators in a way that all AGM revision\u0000operators are included while keeping the original spirit of credibility-limited\u0000revision. Extended credibility-limited revision operators are defined\u0000axiomatically. A semantic characterization of extended credibility-limited\u0000revision operators that employ total preorders on possible worlds is presented.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present efficient circuits for the addition of binary numbers. We assume that we are given arrival times for all input bits and optimize the delay of the circuits, i.e. the time when the last output bit is computed. This contains the classical optimization of depth as a special case where all arrival times are $0$. In this model, we present, among other results, the fastest adder circuits of sub-quadratic size and the fastest adder circuits of linear size. In particular, for adding two $n$-numbers we get a circuits with linear size and delay $log_2W+3log_2log_2n+4log_2log_2log_2n +const$ where $log_2W$ is a lower bound for the delay of any adder circuit (no matter what size it has).
{"title":"Delay-Optimum Adder Circuits with Linear Size","authors":"Ulrich Brenner, Benjamin David Görg","doi":"arxiv-2409.06634","DOIUrl":"https://doi.org/arxiv-2409.06634","url":null,"abstract":"We present efficient circuits for the addition of binary numbers. We assume\u0000that we are given arrival times for all input bits and optimize the delay of\u0000the circuits, i.e. the time when the last output bit is computed. This\u0000contains the classical optimization of depth as a special case where all\u0000arrival times are $0$. In this model, we present, among other results, the\u0000fastest adder circuits of sub-quadratic size and the fastest adder circuits of\u0000linear size. In particular, for adding two $n$-numbers we get a circuits with\u0000linear size and delay $log_2W+3log_2log_2n+4log_2log_2log_2n +const$\u0000where $log_2W$ is a lower bound for the delay of any adder circuit (no matter\u0000what size it has).","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The core challenge in applying abstract interpretation lies in the configuration of abstraction and analysis strategies encoded by a large number of external parameters of static analysis tools. To attain low false-positive rates (i.e., accuracy) while preserving analysis efficiency, tuning the parameters heavily relies on expert knowledge and is thus difficult to automate. In this paper, we present a fully automated framework called Parf to adaptively tune the external parameters of abstract interpretation-based static analyzers. Parf models various types of parameters as random variables subject to probability distributions over latticed parameter spaces. It incrementally refines the probability distributions based on accumulated intermediate results generated by repeatedly sampling and analyzing, thereby ultimately yielding a set of highly accurate parameter settings within a given time budget. We have implemented Parf on top of Frama-C/Eva - an off-the-shelf open-source static analyzer for C programs - and compared it against the expert refinement strategy and Frama-C/Eva's official configurations over the Frama-C OSCS benchmark. Experimental results indicate that Parf achieves the lowest number of false positives on 34/37 (91.9%) program repositories with exclusively best results on 12/37 (32.4%) cases. In particular, Parf exhibits promising performance for analyzing complex, large-scale real-world programs.
{"title":"Parf: Adaptive Parameter Refining for Abstract Interpretation","authors":"Zhongyi Wang, Linyu Yang, Mingshuai Chen, Yixuan Bu, Zhiyang Li, Qiuye Wang, Shengchao Qin, Xiao Yi, Jianwei Yin","doi":"arxiv-2409.05794","DOIUrl":"https://doi.org/arxiv-2409.05794","url":null,"abstract":"The core challenge in applying abstract interpretation lies in the\u0000configuration of abstraction and analysis strategies encoded by a large number\u0000of external parameters of static analysis tools. To attain low false-positive\u0000rates (i.e., accuracy) while preserving analysis efficiency, tuning the\u0000parameters heavily relies on expert knowledge and is thus difficult to\u0000automate. In this paper, we present a fully automated framework called Parf to\u0000adaptively tune the external parameters of abstract interpretation-based static\u0000analyzers. Parf models various types of parameters as random variables subject\u0000to probability distributions over latticed parameter spaces. It incrementally\u0000refines the probability distributions based on accumulated intermediate results\u0000generated by repeatedly sampling and analyzing, thereby ultimately yielding a\u0000set of highly accurate parameter settings within a given time budget. We have\u0000implemented Parf on top of Frama-C/Eva - an off-the-shelf open-source static\u0000analyzer for C programs - and compared it against the expert refinement\u0000strategy and Frama-C/Eva's official configurations over the Frama-C OSCS\u0000benchmark. Experimental results indicate that Parf achieves the lowest number\u0000of false positives on 34/37 (91.9%) program repositories with exclusively best\u0000results on 12/37 (32.4%) cases. In particular, Parf exhibits promising\u0000performance for analyzing complex, large-scale real-world programs.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hybrid games are games played on a finite graph endowed with real variables which may model behaviors of discrete controllers of continuous systems. The synthesis problem for hybrid games is decidable for classical objectives (like LTL formulas) when the games are initialized singular, meaning that the slopes of the continuous variables are piecewise constant and variables are reset whenever their slope changes. The known proof adapts the region construction from timed games. In this paper we show that initialized singular games can be reduced, via a sequence of alternating bisimulations, to timed games, generalizing the known reductions by bisimulation from initialized singular automata to timed automata. Alternating bisimulation is the generalization of bisimulation to games, accomodating a strategy translation lemma by which, when two games are bisimilar and carry the same observations, each strategy in one of the games can be translated to a strategy in the second game such that all the outcomes of the second strategy satisfies the same property that are satisfied by the first strategy. The advantage of the proposed approach is that one may then use realizability tools for timed games to synthesize a winning strategy for a given objective, and then use the strategy translation lemma to obtain a winning strategy in the hybrid game for the same objective.
{"title":"Deciding the synthesis problem for hybrid games through bisimulation","authors":"Catalin Dima, Mariem Hammami, Youssouf Oualhadj, Régine Laleau","doi":"arxiv-2409.05498","DOIUrl":"https://doi.org/arxiv-2409.05498","url":null,"abstract":"Hybrid games are games played on a finite graph endowed with real variables\u0000which may model behaviors of discrete controllers of continuous systems. The\u0000synthesis problem for hybrid games is decidable for classical objectives (like\u0000LTL formulas) when the games are initialized singular, meaning that the slopes\u0000of the continuous variables are piecewise constant and variables are reset\u0000whenever their slope changes. The known proof adapts the region construction\u0000from timed games. In this paper we show that initialized singular games can be\u0000reduced, via a sequence of alternating bisimulations, to timed games,\u0000generalizing the known reductions by bisimulation from initialized singular\u0000automata to timed automata. Alternating bisimulation is the generalization of\u0000bisimulation to games, accomodating a strategy translation lemma by which, when\u0000two games are bisimilar and carry the same observations, each strategy in one\u0000of the games can be translated to a strategy in the second game such that all\u0000the outcomes of the second strategy satisfies the same property that are\u0000satisfied by the first strategy. The advantage of the proposed approach is that\u0000one may then use realizability tools for timed games to synthesize a winning\u0000strategy for a given objective, and then use the strategy translation lemma to\u0000obtain a winning strategy in the hybrid game for the same objective.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yiwen Ding, Krishna Manoorkar, Ni Wayan Switrayni, Ruoding Wang
In this paper, we take first steps toward developing defeasible reasoning on concepts in KLM framework. We define generalizations of cumulative reasoning system C and cumulative reasoning system with loop CL to conceptual setting. We also generalize cumulative models, cumulative ordered models, and preferential models to conceptual setting and show the soundness and completeness results for these models.
在本文中，我们朝着在 KLM 框架下开发概念上的可败推理迈出了第一步。我们定义了概念环境下的累积推理系统 C 和带循环 CL 的累积推理系统的一般化。我们还将累积模型、累积有序模型和优先模型推广到概念环境中，并展示了这些模型的合理性和完备性结果。
{"title":"Defeasible Reasoning on Concepts","authors":"Yiwen Ding, Krishna Manoorkar, Ni Wayan Switrayni, Ruoding Wang","doi":"arxiv-2409.04887","DOIUrl":"https://doi.org/arxiv-2409.04887","url":null,"abstract":"In this paper, we take first steps toward developing defeasible reasoning on\u0000concepts in KLM framework. We define generalizations of cumulative reasoning\u0000system C and cumulative reasoning system with loop CL to conceptual setting. We\u0000also generalize cumulative models, cumulative ordered models, and preferential\u0000models to conceptual setting and show the soundness and completeness results\u0000for these models.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"131 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mario Alviano, Laura Giordano, Daniele Theseider Dupré
In this paper we propose a many-valued temporal conditional logic. We start from a many-valued logic with typicality, and extend it with the temporal operators of the Linear Time Temporal Logic (LTL), thus providing a formalism which is able to capture the dynamics of a system, trough strict and defeasible temporal properties. We also consider an instantiation of the formalism for gradual argumentation.
{"title":"Temporal Many-valued Conditional Logics: a Preliminary Report","authors":"Mario Alviano, Laura Giordano, Daniele Theseider Dupré","doi":"arxiv-2409.09069","DOIUrl":"https://doi.org/arxiv-2409.09069","url":null,"abstract":"In this paper we propose a many-valued temporal conditional logic. We start\u0000from a many-valued logic with typicality, and extend it with the temporal\u0000operators of the Linear Time Temporal Logic (LTL), thus providing a formalism\u0000which is able to capture the dynamics of a system, trough strict and defeasible\u0000temporal properties. We also consider an instantiation of the formalism for\u0000gradual argumentation.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142267203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We try to clarify the relationship between computation and concurrency. Base on the so-called truly concurrent automata, we introduce communication and more operators, and establish the algebras modulo language equivalence and bisimilarity.
{"title":"Computation and Concurrency","authors":"Yong Wang","doi":"arxiv-2409.02595","DOIUrl":"https://doi.org/arxiv-2409.02595","url":null,"abstract":"We try to clarify the relationship between computation and concurrency. Base\u0000on the so-called truly concurrent automata, we introduce communication and more\u0000operators, and establish the algebras modulo language equivalence and\u0000bisimilarity.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently, the description logic LE-$mathcal{ALC}$ was introduced for reasoning in the semantic environment of the enriched formal contexts, and a tableaux algorithm was developed for checking the consistency of ABoxes in this logic cite{van2023non}. In this paper, we study the ontology-mediated query answering in LE-$mathcal{ALC}$. In particular, we show that several different types of queries can be answered efficiently for LE-$mathcal{ALC}$ knowledge bases with acyclic TBoxes using our tableaux algorithm directly or by extending it with some additional rules.
{"title":"Query answering in lattice-based description logic","authors":"Krishna Manoorkar, Ruoding Wang","doi":"arxiv-2409.02289","DOIUrl":"https://doi.org/arxiv-2409.02289","url":null,"abstract":"Recently, the description logic LE-$mathcal{ALC}$ was introduced for\u0000reasoning in the semantic environment of the enriched formal contexts, and a\u0000tableaux algorithm was developed for checking the consistency of ABoxes in this\u0000logic cite{van2023non}. In this paper, we study the ontology-mediated query\u0000answering in LE-$mathcal{ALC}$. In particular, we show that several different\u0000types of queries can be answered efficiently for LE-$mathcal{ALC}$ knowledge\u0000bases with acyclic TBoxes using our tableaux algorithm directly or by extending\u0000it with some additional rules.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Ho-Zhao problem asks whether any two dcpo's with isomorphic Scott closed set lattices are themselves isomorphic, that is, whether the category $mathbf{DCPO}$ of dcpo's and Scott-continuous maps is $Gamma$-faithful. In 2018, Ho, Goubault-Larrecq, Jung and Xi answered this question in the negative, and they introduced the category $mathbf{DOMI}$ of dominated dcpo's and proved that it is {$Gamma$-faithful}. Dominated dcpo's subsume many familiar families of dcpo's in domain theory, such as the category of bounded-complete dcpo's and that of sober dcpo's, among others. However, it is unknown whether the category of dominated dcpo's dominates all well-filtered dcpo's, a class strictly larger than that of bounded-complete lattices and that of sober dcpo's. In this paper, we address this very natural question and show that the category $mathbf{WF}$ of well-filtered dcpo's is not $Gamma$-faithful, and as a result of it, well-filtered dcpo's need not be dominated in general. Since not all dcpo's are well-filtered, our work refines the results of Ho, Goubault-Larrecq, Jung and Xi. As a second contribution, we confirm that the Lawson's category of $Omega^{*}$-compact dcpo's is $Gamma$-faithful. Moreover, we locate a class of dcpo's which we call weakly dominated dcpo's, and show that this class is $Gamma$-faithful and strictly larger than $mathbf{DOMI}$.
{"title":"The category of well-filtered dcpos is not $Γ$-faithful","authors":"Hualin Miao, Huijun Hou, Xiaodong Jia, Qingguo Li","doi":"arxiv-2409.01546","DOIUrl":"https://doi.org/arxiv-2409.01546","url":null,"abstract":"The Ho-Zhao problem asks whether any two dcpo's with isomorphic Scott closed\u0000set lattices are themselves isomorphic, that is, whether the category\u0000$mathbf{DCPO}$ of dcpo's and Scott-continuous maps is $Gamma$-faithful. In\u00002018, Ho, Goubault-Larrecq, Jung and Xi answered this question in the negative,\u0000and they introduced the category $mathbf{DOMI}$ of dominated dcpo's and proved\u0000that it is {$Gamma$-faithful}. Dominated dcpo's subsume many familiar families\u0000of dcpo's in domain theory, such as the category of bounded-complete dcpo's and\u0000that of sober dcpo's, among others. However, it is unknown whether the category\u0000of dominated dcpo's dominates all well-filtered dcpo's, a class strictly larger\u0000than that of bounded-complete lattices and that of sober dcpo's. In this paper,\u0000we address this very natural question and show that the category $mathbf{WF}$\u0000of well-filtered dcpo's is not $Gamma$-faithful, and as a result of it,\u0000well-filtered dcpo's need not be dominated in general. Since not all dcpo's are\u0000well-filtered, our work refines the results of Ho, Goubault-Larrecq, Jung and\u0000Xi. As a second contribution, we confirm that the Lawson's category of\u0000$Omega^{*}$-compact dcpo's is $Gamma$-faithful. Moreover, we locate a class\u0000of dcpo's which we call weakly dominated dcpo's, and show that this class is\u0000$Gamma$-faithful and strictly larger than $mathbf{DOMI}$.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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