J. Log. Comput.Pub Date : 2019-12-20DOI: 10.1093/LOGCOM/EXV084
Andreea Achimescu, A. Baltag, J. Sack
{"title":"The probabilistic logic of communication and change","authors":"Andreea Achimescu, A. Baltag, J. Sack","doi":"10.1093/LOGCOM/EXV084","DOIUrl":"https://doi.org/10.1093/LOGCOM/EXV084","url":null,"abstract":"This article introduces a Probabilistic Logic of Communication and Change, which captures in a unified framework subjective probability, arbitrary levels of mutual knowledge and a mechanism for multi-agent Bayesian updates that can model complex social-epistemic scenarios, such as informational cascades. We show soundness, completeness and decidability of our logic, and apply it to a concrete example of cascade.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"146 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114347977","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}
J. Log. Comput.Pub Date : 2019-12-10DOI: 10.1093/logcom/exz019
Stephane Demri, Raul Fervari
{"title":"The power of modal separation logics","authors":"Stephane Demri, Raul Fervari","doi":"10.1093/logcom/exz019","DOIUrl":"https://doi.org/10.1093/logcom/exz019","url":null,"abstract":"We introduce a modal separation logic MSL whose models are memory states from separation logic and the logical connectives include modal operators as well as separating conjunction and implication from separation logic. With such a combination of operators, some fragments of MSL can be seen as genuine modal logics whereas some others capture standard separation logics, leading to an original language to speak about memory states. We analyse the decidability status and the computational complexity of several fragments of MSL, obtaining surprising results by design of proof methods that take into account the modal and separation features of MSL. For example, the satisfiability problem for the fragment of MSL with 3, the difference modality 〈6 =〉 and separating conjunction ∗ is shown Tower-complete whereas the restriction either to 3 and ∗ or to 〈6=〉 and ∗, is only NP-complete. We establish that the full logic MSL admits an undecidable satisfiability problem. Furthermore, we investigate variants of MSL with alternative semantics and we build bridges with interval temporal logics and with logics equipped with sabotage operators.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122811989","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}
J. Log. Comput.Pub Date : 2019-12-02DOI: 10.1093/LOGCOM/EXZ017
Xiaojuan Liao, M. Koshimura
{"title":"A comparative analysis and improvement of MaxSAT encodings for coalition structure generation under MC-nets","authors":"Xiaojuan Liao, M. Koshimura","doi":"10.1093/LOGCOM/EXZ017","DOIUrl":"https://doi.org/10.1093/LOGCOM/EXZ017","url":null,"abstract":"\u0000 Coalition structure generation (CSG) is one of the main research issues in the use of coalitional games in multiagent systems and weighted partial MaxSAT (WPM) encodings, i.e. rule relation-based WPM (RWPM) and agent relation-based WPM (AWPM), which are efficient for solving the CSG problem. Existing studies show that AWPM surpasses RWPM since it achieves more compact encoding; it generates fewer variables and clauses than RWPM. However, in this paper, we focus on a special case in which the two encodings generate identical numbers of variables and clauses. Experiments show that RWPM surprisingly has a dominant advantage over AWPM, which aroused our interest. We exploit the deep-rooted reason and find that it is the redundancy when encoding transitive laws in RWPM that leads to this situation. Finally, we remove redundant clauses for transitive laws in RWPM and develop an improved RWPM with refined transitive laws to solve the CSG problem. Experiments demonstrate that refined encoding is more compact and efficient than previous WPM encodings.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115433136","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}
J. Log. Comput.Pub Date : 2019-12-02DOI: 10.1093/LOGCOM/EXZ018
M. Collinson
{"title":"A logic of hypothetical conjunction","authors":"M. Collinson","doi":"10.1093/LOGCOM/EXZ018","DOIUrl":"https://doi.org/10.1093/LOGCOM/EXZ018","url":null,"abstract":"\u0000 A binary connective that can be read as a matching conjunction for conditional connectives found in many conditional logics is considered. The most natural way to read this connective is often as a conjunction and yet, hypothetically, considered to hold of a state of affairs that could be obtained under the hypothesis. The connective can be given an intensional semantics extending a standard semantics of conditional logic that uses propositionally indexed families of binary relations on possible worlds. This semantics is determined by an adjoint relationship between the operations supporting the semantics of the conditional and the new conjunction. The semantics of the hypothetical conjunction connective subsumes the semantics, supported by a ternary relation semantics, of the fusion connective that arises in connection with substructural and relevant logics, and therefore subsumes a number of other forms of conjunction. A number of applications of the hypothetical conjunction connective are discussed, including generalized forms of resource reasoning used in computer science applications.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116888735","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}
J. Log. Comput.Pub Date : 2019-12-02DOI: 10.1093/logcom/exz014
G. Primiero
{"title":"A logic of efficient and optimal designs","authors":"G. Primiero","doi":"10.1093/logcom/exz014","DOIUrl":"https://doi.org/10.1093/logcom/exz014","url":null,"abstract":"\u0000 Logics of design have been formulated until recently to offer systematic treatments of the way systems express the relation between resources, processes and their outputs. We present a logic of systems design which explicitly formalizes this relation as a decidable checking problem on resource access and define computable efficiency and optimality properties.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134638146","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}
J. Log. Comput.Pub Date : 2019-12-01DOI: 10.1093/logcom/exz020
Linh Anh Nguyen
{"title":"The Influence of the Test Operator on the Expressive Powers of PDL-Like Logics","authors":"Linh Anh Nguyen","doi":"10.1093/logcom/exz020","DOIUrl":"https://doi.org/10.1093/logcom/exz020","url":null,"abstract":"\u0000 Berman and Paterson proved that test-free propositional dynamic logic (PDL) is weaker than PDL. One would raise questions: does a similar result also hold for extensions of PDL? For example, is test-free converse-PDL (CPDL) weaker than CPDL? In what circumstances the test operator can be eliminated without reducing the expressive power of a PDL-based logical formalism? These problems have not yet been studied. As the description logics $mathcal{ALC}_{trans}$ and $mathcal{ALC}_{reg}$ are, respectively, variants of test-free PDL and PDL, there is a concept of $mathcal{ALC}_{reg}$ that is not equivalent to any concept of $mathcal{ALC}_{trans}$. Generalizing this, we prove that there is a concept of $mathcal{ALC}_{reg}$ that is not equivalent to any concept of the logic that extends $mathcal{ALC}_{trans}$ with inverse roles, nominals, qualified number restrictions, the universal role and local reflexivity of roles. We also provide some results for the case with RBoxes and TBoxes. One of them states that tests can be eliminated from TBoxes of the deterministic Horn fragment of $mathcal{ALC}_{reg}$.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117319288","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}
J. Log. Comput.Pub Date : 2019-12-01DOI: 10.1093/logcom/exz025
L. Hella, Miikka Vilander
{"title":"Formula size games for modal logic and μ-calculus","authors":"L. Hella, Miikka Vilander","doi":"10.1093/logcom/exz025","DOIUrl":"https://doi.org/10.1093/logcom/exz025","url":null,"abstract":"We propose a new version of formula size game for modal logic. The game characterizes the equivalence of pointed Kripke models up to formulas of given numbers of modal operators and binary connectives. Our game is similar to the well-known Adler–Immerman game. However, due to a crucial difference in the definition of positions of the game, its winning condition is simpler, and the second player does not have a trivial optimal strategy. Thus, unlike the Adler–Immerman game, our game is a genuine two-person game. We illustrate the use of the game by proving a non-elementary succinctness gap between bisimulation invariant first-order logic $textrm{FO}$ and (basic) modal logic $textrm{ML}$. We also present a version of the game for the modal $mu $-calculus $textrm{L}_mu $ and show that $textrm{FO}$ is also non-elementarily more succinct than $textrm{L}_mu $.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124908216","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}
J. Log. Comput.Pub Date : 2019-10-06DOI: 10.1093/logcom/exaa049
D. Normann, Sam Sanders
{"title":"Open sets in computability theory and reverse mathematics","authors":"D. Normann, Sam Sanders","doi":"10.1093/logcom/exaa049","DOIUrl":"https://doi.org/10.1093/logcom/exaa049","url":null,"abstract":"To enable the study of open sets in computational approaches to mathematics, lots of extra data and structure on these sets is assumed. For both foundational and mathematical reasons, it is then a natural question, and the subject of this paper, what the influence of this extra data and structure is on the logical and computational properties of basic theorems pertaining to open sets. To answer this question, we study various basic theorems of analysis, like the Baire category, Heine, Heine-Borel, Urysohn, and Tietze theorems, all for open sets given by their (third-order) characteristic functions. Regarding computability theory, the objects claimed to exist by the aforementioned theorems undergo a shift from `computable' to `not computable in any type two functional', following Kleene's S1-S9. Regarding Reverse Mathematics, the latter's so-called Main Question, namely which set existence axioms are necessary for proving a given theorem, does not have an unique or unambiguous answer for the aforementioned theorems, working in Kohlenbach's higher-order framework. A finer study of representations of open sets leads to the new `$Delta$-functional' which has unique (computational) properties.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133158605","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}
J. Log. Comput.Pub Date : 2019-09-20DOI: 10.1093/logcom/exaa023
U. Andrews, N. Schweber, A. Sorbi
{"title":"Self-full ceers and the uniform join operator","authors":"U. Andrews, N. Schweber, A. Sorbi","doi":"10.1093/logcom/exaa023","DOIUrl":"https://doi.org/10.1093/logcom/exaa023","url":null,"abstract":"\u0000 A computably enumerable equivalence relation (ceer) $X$ is called self-full if whenever $f$ is a reduction of $X$ to $X$, then the range of $f$ intersects all $X$-equivalence classes. It is known that the infinite self-full ceers properly contain the dark ceers, i.e. the infinite ceers which do not admit an infinite computably enumerable transversal. Unlike the collection of dark ceers, which are closed under the operation of uniform join, we answer a question from [ 4] by showing that there are self-full ceers $X$ and $Y$ so that their uniform join $Xoplus Y$ is non-self-full. We then define and examine the hereditarily self-full ceers, which are the self-full ceers $X$ so that for any self-full $Y$, $Xoplus Y$ is also self-full: we show that they are closed under uniform join and that every non-universal degree in ${operatorname{textbf{Ceers}}}_{operatorname{{mathcal{I}}}}$ have infinitely many incomparable hereditarily self-full strong minimal covers. In particular, every non-universal ceer is bounded by a hereditarily self-full ceer. Thus, the hereditarily self-full ceers form a properly intermediate class in between the dark ceers and the infinite self-full ceers, which is closed under $oplus $.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"506 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133817359","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}
J. Log. Comput.Pub Date : 2019-09-16DOI: 10.1093/logcom/exz024
D. Galmiche, P. Kimmel, D. Pym
{"title":"A Substructural Epistemic Resource Logic: Theory and Modelling Applications","authors":"D. Galmiche, P. Kimmel, D. Pym","doi":"10.1093/logcom/exz024","DOIUrl":"https://doi.org/10.1093/logcom/exz024","url":null,"abstract":"We present a substructural epistemic logic, based on Boolean BI, in which the epistemic modalities are parametrized on agents’ local resources. The new modalities can be seen as generalizations of the usual epistemic modalities. The logic combines Boolean BI’s resource semantics—we introduce BI and its resource semantics at some length—with epistemic agency. We illustrate the use of the logic in systems modelling by discussing some examples about access control, including semaphores, using resource tokens. We also give a labelled tableaux calculus and establish soundness and completeness with respect to the resource semantics.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122327063","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}