Alonso-Meijide and Fiestras-Janeiro (2002, Annals of Operations Research 109, 213–227) proposed a modification of the Banzhaf value for games where a coalition structure is given. In this paper we present a method to compute this value by means of the multilinear extension of the game. A real-world numerical example illustrates the application procedure.

This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of linear logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic linear logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class of (...) Kripke resource models extended with a neighbourhood function: modal Kripke resource models. We propose a Hilbert-style axiomatisation and a Gentzen-style sequent calculus. We show that the proof theories are sound and complete with respect to the class of modal Kripke resource models. We show that the sequent calculus admits cut elimination and that proof-search is in PSPACE. We then show how to extend the results when non-commutative connectives are added to the language. Finally, we put the l.. (shrink)

We introduce the notion of τ-like partial order, where τ is one of the linear order types ω, ω*, ω + ω*, and ζ. For example, being ω-like means that every element has finitely many predecessors, while being ζ-like means that every interval is finite. We consider statements of the form “any τ-like partial order has a τ-like linear extension” and “any τ-like partial order is embeddable into τ” . Working in the framework of reverse mathematics, we (...) show that these statements are equivalent either to equation image or to equation image over the usual base system equation image. (shrink)

Let E be a subset of. A linear extension operator is a linear map that sends a function on E to its extension on some superset of E. In this paper, we show that if E is a semi‐algebraic or subanalytic subset of, then there is a linear extension operator such that is semi‐algebraic (subanalytic) whenever f is semi‐algebraic (subanalytic).

We show that the maximal linear extension theorem for well partial orders is equivalent over RCA0 to ATR0. Analogously, the maximal chain theorem for well partial orders is equivalent to ATR0 over RCA0.

Pretabularity is the attribute of logics that are not characterised by finite matrices, but all of whose proper extensions are. Two of the first-known pretabular logics were Dummett’s famous super-...

The closed world assumption plays a fundamental role in the theory of deductive databases. On the other hand, multi-valued logics occupy a vast field in non-classical logics. Some questions are better explained and expressed in terms of such logics. To enhance the expressive power and the declarative ability of a deductive database, we extend various CWA formalizations, including the naive CWA, the generalized CWA and the careful CWA, to multi-valued logics. The basic idea is to embed logic formulae (...) into some polynomial ring. The extensions can be applied in a uniform manner to any finitely multi-valued logics. Therefore they have also computational interest. (shrink)

The feasible interpolation theorem for semantic derivations from [J. Krajíček, Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic, J. Symbolic Logic 62 457–486] allows to derive from some short semantic derivations of the disjointness of two [Formula: see text] sets [Formula: see text] and [Formula: see text] a small communication protocol computing the Karchmer–Wigderson multi-function [Formula: see text] associated with the sets, and such a protocol further yields a small circuit separating [Formula: see text] (...) from [Formula: see text]. When [Formula: see text] is closed upwards, the protocol computes the monotone Karchmer–Wigderson multi-function [Formula: see text] and the resulting circuit is monotone. Krajíček [Interpolation by a game, Math. Logic Quart. 44 450–458] extended the feasible interpolation theorem to a larger class of semantic derivations using the notion of a real communication complexity. In this paper, we generalize the method to a still larger class of semantic derivations by allowing randomized protocols. We also introduce an extension of the monotone circuit model, monotone circuits with a local oracle, that does correspond to communication protocols for [Formula: see text] making errors. The new randomized feasible interpolation thus shows that a short semantic derivation of the disjointness of [Formula: see text], [Formula: see text] closed upwards, yields a small randomized protocol for [Formula: see text] and hence a small monotone CLO separating the two sets. This research is motivated by the open problem to establish a lower bound for proof system [Formula: see text] operating with clauses formed by linear Boolean functions over [Formula: see text]. The new randomized feasible interpolation applies to this proof system and also to cutting planes CP, to small width resolution over CP of Krajíček [Discretely ordered modules as a first-order extension of the cutting planes proof system, J. Symbolic Logic 63 1582–1596] ) and to random resolution RR of Buss, Kolodziejczyk and Thapen [Fragments of approximate counting, J. Symbolic Logic 79 496–525]. The method does not yield yet lengths-of-proofs lower bounds; for this it is necessary to establish lower bounds for randomized protocols or for monotone CLOs. (shrink)

We show that every model of IΔ0 has an end extension to a model of a theory where log-space computable function are formalizable. We also show the existence of an isomorphism between models of IΔ0 and models of linear arithmetic LA.

In this paper we analyze some aspects of the question of using methods from model theory to study structures of functional analysis.By a well known result of P. Lindström, one cannot extend the expressive power of first order logic and yet preserve its most outstanding model theoretic characteristics (e.g., compactness and the Löwenheim-Skolem theorem). However, one may consider extending the scope of first order in a different sense, specifically, by expanding the class of structures that are regarded as models (e.g., (...) including Banach algebras or other structures of functional analysis), and ask whether the resulting extensions of first order model theory preserve some of its desirable characteristics.A formal framework for the study of structures based on Banach spaces from the perspective of model theory was first introduced by C. W. Henson in [8] and [6]. Notions of syntax and semantics for these structures were defined, and it was shown that using them one obtains a model theoretic apparatus that satisfies many of the fundamental properties of first order model theory. For instance, one has compactness, Löwenheim-Skolem, and omitting types theorems. Further aspects of the theory, namely, the fundamentals of stability and forking, were first introduced in [10] and [9].The classes of mathematical structures formally encompassed by this framework are normed linear spaces, possibly expanded with additional structure,e.g., operations, real-valued relations, and constants. This notion subsumes wide classes of structures from functional analysis. However, the restriction that the universe of a structure be a normed space is not necessary. (This restriction has a historical, rather than technical origin; specifically, the development of the theory was originally motivated by questions in Banach space geometry.) Analogous techniques can be applied if the universe is a metric space. Now, when the underlying metric topology is discrete, the resulting model theory coincides with first order model theory, so this logic extends first order in the sense described above. Furthermore, without any cost in the mathematical complexity, one can also work in multi-sorted contexts, so, for instance, one sort could be an operator algebra while another is. say, a metric space. (shrink)

In this paper, we develop the system LZF of set theory with the unrestricted comprehension in full linear logic and show that LZF is a conservative extension of ZF– i.e., the Zermelo-Fraenkel set theory without the axiom of regularity. We formulate LZF as a sequent calculus with abstraction terms and prove the partial cut-elimination theorem for it. The cut-elimination result ensures the subterm property for those formulas which contain only terms corresponding to sets in ZF–. This implies that (...) LZF is a conservative extension of ZF– and therefore the former is consistent relative to the latter. (shrink)

This paper provides a computational framework, based on defeasible logic, to capture some aspects of institutional agency. Our background is Kanger-Lindahl-Pörn account of organised interaction, which describes this interaction within a multi-modal logical setting. This work focuses in particular on the notions of counts-as link and on those of attempt and of personal and direct action to realise states of affairs. We show how standard defeasible logic (DL) can be extended to represent these concepts: the resulting system preserves some (...) basic properties commonly attributed to them. In addition, the framework enjoys nice computational properties, as it turns out that the extension of any theory can be computed in time linear to the size of the theory itself. (shrink)

This wide ranging discourse covers many disciplines of science and the human condition in an attempt to fully understand the manifestation of time. Time's Paradigm is, at its inception, a philosophical debate between the theories of 'Presentism' and 'The Block Model', beginning with a pronounced psychological analysis of 'free will' in an environment where the past and the future already exist. It lays the foundation for the argument that time is a cyclical, contained progression, rather than a meandering voyage into (...) infinity, bringing into question the validity of a commensurate 'Big Bang'. Following, the proposal widens to encompass physics. It tackles clock rates and time dilation, acausality and the nuisance of a universal clock, and demonstrates that conscious consideration creates the present moment - time's flow - separating the solid state past and future whose reality is devoid of space. Arguments relating to Quantum Physics theory, including the Uncertainty Principle and a Superposition of States, lend credibility to key areas involving cognitive awareness. It is posited that defined points in time and space prohibit progress in linear models for progression. Thus motile paradoxes can be resolved with the absence of infinities; temporal perception, it is concluded, being the result of uncertainty. Time's Paradigm takes the bold step of asking us to consider a tangible dimension of time, representing an intimate extension of our three, known spatial dimensions. Chaos theory is briefly introduced leading to the configuration of a fractal fourth dimension of time whose assumption demands only one direction of flow. Further, it asks whether our universe is expanding or contracting. It considers the simple physics of bodies contracting in a fourth dimension of time (UC), and how that marries comfortably with standard scientific models such as Special Relativity. The rate at which matter is contracting in the universe is illustrated in a reduction factor of 1.618... coinciding with Fibonacci's Ratio and countering Time Dilation. Lastly the more complex aspects of relativistic velocities are tackled together with the conundrum of Zero Velocity and The Speed of Light being attributes of the same event in Cyclical Space-Time, and ultimately, the prospect of superluminal velocities by interaction with parallel time-zones in a multi-layered block universe. (shrink)

The trend to centralization of the Mizrahi narrative has become an integral part of the nationalistic, ethnic, religious, and ideological-political dimensions of the emerging, complex Israeli identity. This trend includes several forms of opposition: strong opposition to "melting pot" policies and their ideological leaders; opposition to the view that ethnicity is a dimension of the tension and schisms that threaten Israeli society; and, direct repulsion of attempts to silence and to dismiss Mizrahim and so marginalize them hegemonically. The Mizrahi Democratic (...) Rainbow [The Keshet], the most prominent proponent and representative of this trend, was established in the 1990s with the intention of being a leading civic and political body in Israeli society. While it was the Mizrahi worldview that led to selection of the organization's name and aims, their vision was to be involved in social struggle on behalf of other groups in Israeli society. Since it was established, The Keshet has aimed to function as an assertive, long-term alternative coalition exerting influence, power, and pressure on the Israeli narrative network. And, indeed, the organization has succeeded in disrupting Israeli discourse, principally, by challenging the ideological foundations of the Zionist meta-narrative. Nearing the end of the first decade of the 21st century and nearly a decade since it was established, The Keshet not only represents the most current wave of Mizrahi discourse, it has changed it to such a great degree that it is impossible to ignore its influence. Further, this alternative narrative may have significant potential to advance the internal Jewish discourse so fundamental at this time given the changing Israeli situation and regional conditions. And, while it is possible to view The Keshet and this new narrative as a continuation of the Mizrahi struggle, as a narrative The Keshet's agenda represents a post-colonial perspective and multi-cultural alternative to Zionism as a social vehicle. Amidst all of this, The Keshet continues to offer concrete proposals to change the Jewish character of the state as well as its internal and external relations. One of the primary goals of this study was to examine the rise of the Mizrahi narrative over the last two decades and the new Mizrahi discourse in Israeli society. More specifically, the study sought to attain an in-depth understanding of the central narrative created and represented by The Keshet. An additional goal was to investigate the influence of The Keshet's activity and the narrative it constructed in regard to other narratives. In particular, the study focused on The Keshet's opposition to the central Zionist narrative that infuses civic, political, and academic frameworks in Israel. Accordingly, the primary research questions investigated in the study sought to determine: What has been the influence of the Mizrahi Democratic Rainbow on the Mizrahi narrative in Israel? And, what are implications of such influence for the central Zionist narrative? Methodologically, the study was based on narrative and comparative analyses of texts from different periods of the older and newer Mizrahi narratives. The corpus included two types of texts: First, academic texts and opinion pieces, both philosophical and programmatic in nature, published in magazines, journals, books, as well as position papers; second, all of the texts published by prominent and influential figures who charted the path of The Keshet or led it organizationally and/or intellectually over the last twenty years (e. g., Yehudah Shenhav, Yossi Yona, Moshe Krief among others). All texts were examined by means of philosophical, historical and critical hermeneutic tools. This analysis revealed different levels of Mizrahi and civic discourse in Israel as well as among The Keshet's founders and leading ideologues. The study was based on a three stage process model, developed for purposes of this study, for investigation and analysis of the new Mizrahi narrative as well as other oppositional narratives, in particular opposition to the hegemonic meta-narrative. The stages are: issuing the challenge, dissolution and, liberation; that is, liberation is the measure of the ultimate success of the struggle for narrative change. Such change is not based on success in the field, but rather on a radical, fundamental reversal of thought, discourse patterns, stylistic structures, as well as forms of questioning - in this case of taken-for-granted racist mechanisms. However, the principal change is in achieving a deep, inner de-legitimization of the signifiers, categories, and reproductions of all manner of mockery that are based on immoral colonialist processes that are reinforced by regimes of fear and intimidation whose self-destruction began upon their very creation. This three stage model charts the course of the oppositional Mizrahi narrative from: accounting for the past (passing judgment on the so-called historic colonialist Zionism) to writing a new (pure Mizrahi) history and creation of a Mizrahi-Arab identity separate from the Ashkenazic, identified as Zionist. Contemporary post-colonialist discourse is integral in these stages. Such a perspective has been transformed by transitions from - binarism to hybridity, Orientalism to Occidentalism, the politics of "liberation" to "constructive" politics, from the history of consciousness to the history of change, as well as from nationalist to post-nationalist questions. Fundamentally, according to this approach, political and other struggles for the emerging narrative of Mizrahi (or Arab) history seek to centralize it in society and weave it amidst the models of multiculturalism. Undertaken in parallel, the central characteristics of all these stages are borrowed from countries in which the need for national reconciliation led to renunciation of apartheid and racist policies and historical judgment of the hegemony supported by racist leaders. In addition, these three moves were undertaken in Keshet and its ideologues by means of substantive symbolic violence directed at the hegemonic Ashkenazic discourse, which included creation of hatred of it, use of stereotypes the opposite of oppressive discourse, and adoption of an arrogant point of view toward it. This stands in stark contrast to the claims of the self-proclaimed new Mizrahi stance of a discourse established on purely ethical grounds that sought to cleanse itself of these very same oppressive elements. The model developed for and demonstrated in this study allows for analysis of oppositional narratives in which the libratory stage evolves into a form of entrapment, as appears to be occurring to the new Mizrahi discourse. This conclusion is based on the observations shared by many Keshet proponents including leading intellectuals who worked on the manifestos that were the subject of criticism from the Zionist camp. The study identified and defined the following six interwoven strata, which for purposes of explication are each discussed in a separate chapter: The first chapter presents a general theoretical discussion of the issue of the narrative and the inter-narrative struggle that has become central and applicable in various ways in the latest generation (e. g., anthropologically, hermeneutically, and philosophically). The analysis surveys different discussions in the inter-narrative struggle and locates them in the contexts, relations, and meanings derived from, representing, and indeed reproducing the narrative of national identity. The second chapter includes a historical survey of the older Mizrahi struggle that existed prior to the ascendance of the new Mizrahi narrative. Initially, Mizrahi discourse focused on expressing the ethnic protest that grew in years to follow. These feelings of discrimination and social distancing of the immigrants from Islamic countries gave birth to expressions of protest, the most prominent of which were Wadi Salib and the Black Panther Movement's various activities. The research literature contains many explanations for the exacerbation of the ethnic problem and creation of a situation that could not be ignored. The consensus academic view reached at the end of the 1970s identified a number of primary factors for this situation: the existence and extensive numbers of different ethnic groups; the relative or absolute segregation of frameworks within which members of these ethnic groups lived and acted; and the significant overlap between socio-economic status and feelings of discrimination retained by members of the Mizrahi group due years of neglect by the Ashkenazic establishment, the strengthening of Mizrahi social, cultural, and political power, as well as the emergence of a Mizrahi elite that identified with Mizrahi problems. The severe consequences of feelings of discrimination were expressed in a long series of events, such as: rioting by residents of the Rehovot Sharayim neighborhood in 1956; events of Wadi Salib in Haifa in 1959; and a chain of activities involving the Black Panthers in the 1970s. Protest was also an aspect of the "tent movement" in the 1970s and 1980s. Political activities were advanced by the Tami Movement that competed in the election for the 10th Knesset in 1981 and the Shas Movement that has continued to garner political power since being found in 1984. The 1980s and 1990s were characterized as the era of radical consciousness of Mizrahi discourse as well as by the rise to power, in consecutive order, of the political parties – Tami, Shas, and the Mizrahim HaHadashim [the New Mizrahi]. The latter party laid the foundations of the new radical Mizrahi discourse from which emerged such cultural activities as: Iton Aher [A Different Newspaper]; Bimat Kivon Aher [Another Direction Forum]; Efir'yon journal; the Halah Organization for Education in Neighborhoods, Development Towns, and Villages; Kedma; the newspaper – Patish [Hammer]; and, eventually the establishment of Keshet. The third chapter presents an examination of the materialization of the inter-narrative struggle in the case of Israel, with a specific focus on The Keshet and the new Mizrahi narrative advanced by it and intellectuals. The Keshet ideology is examined in the context of its grounding in post-colonial thought, especially that of Edward Said; the directions proposed by Ella Shohat and her followers; the central thinkers of the narrative in Israel in the last decade; and the harsh critique leveled at the Ashkenazic-Zionist narrative. The practical steps proposed for implementation within the multicultural model are also examined. Here the effort to reduce the centrality of Zionism while revealing its oppressive mechanisms was undertaken in parallel with use of these mechanisms in order to create a Mizrahi space with broad margins inclusive of alternative forms of Israeli identity in the Middle East and in conjunction with Arabs within and beyond Israel. Mizrahi traditionalism is examined in the fourth chapter in two particular respects. First, the criticism of the new Mizrahi narrative leveled by the renewed view and, second, the implications of the alternative in terms of creating a Mizrahi space that does not oppose Zionism. Rather, in opposing the post-colonialist perspective, this renewed traditionalist perspective criticizes as well as values Zionism. This space seeks to be both Jewish and Mizrahi. It does not detach itself from nationalist Zionism but rather views itself as a continuation of this tradition and, accordingly, is an effort to develop a next stage in its development. For example, an essential dimension of the traditionalist perspective, "commitment," is considered in this stage to be a fertile basis for dialogue with the past and as an anchor for contemporary interpretation of Mizrahi and other Jews' identities in Israel. The fifth and sixth chapters deal with all of the vectors of criticism directed at the new Mizrahi narrative, including its ideological foundations, philosophical stance, as well as intellectual and practical basis in the Israeli sphere in the face of Palestinian nationalism. These vectors of criticism from within and beyond The Keshet deal with issues, such as, the meaning of the movement's activities and the narrative that it offers regarding questions of Israeli identity, Israeli collective memory, and Mizrahi self-perception. At the same time, it must confront the capitalist neo-liberal narrative in a global world and thrive in a context in which it must make itself manifest amidst oppositional narratives. The final chapter presents a comprehensive, critical analysis of the new Mizrahi narrative. It does so by means of a theoretical model that examines it as an oppositional narrative – one that seeks to challenge the hegemonic meta-narrative, to dissolve the boundaries of the narrative discourse, and to propose liberation and redemption that may led to entrapment amidst a changing, a-dichotomous realities (e. g., global economic development in the face of Zionist nationalisms that display ideological strength as well as development of the sense of being an Israeli that maintains its vitality and continuity while being constituted by sectors that challenge being a Mizrahi, such as co-ethnic subjects. The Keshet's influence is dramatic and extends in a number of central directions. Its political activity and non-entry into the domains of the Israeli parliament granted the movement significant power in civic discourse and contributed to changing the persona of the Mizrahi discourse; for example, from political-party struggles over budgets and obtaining shares of the regime to changing the face of Israeli society and the centrality of the Mizrahi narrative. This change included deconstructing the Ashkenazic narrative and constructing comprehensive Ashkenazic-Zionist guilt, as evident in the Ehud Barak's request for collective forgiveness. This was accomplished through the participation of leading members of Keshet who appeared in prominent intellectual forums and engaged in lively discourse - principally in academic, social, and media domains. Such participation gave new meaning to various aspects of Israeli society while establishing different models of multiculturalism. The rise of the new Mizrahi narrative is a significant marker in the inter-narrative struggle as it represents a desire for separate or hybrid identities. And, the deep probing of the narrative constructed by leaders of The Keshet and those who identify with the movement produced a number of clear ways to distinguish it from the old Mizrahi struggle, whose history was portrayed through social protests, in a manner similar to linear vectors marked with wars and elections. The old Mizrahi struggle selected the traditional tactical struggle identified usually with social and political movements that seek to change political, social, and economic reality - from the bottom up. Their primary demand was to change decisions as well as the division of social goods and resources. Hence, this older period of struggle was not aimed at opposing the ideological foundations of the hegemonic narrative nor did it seek to undermine in a radical manner the unique nature of the state of Israel as a revolutionary solution for the problems of the Jews according to the Zionist approach, as a national home for the Jewish people, and recognition of the right to an preferred and meta-definition of Jewish nationalism. In contrast, the top down struggle advanced by the new narrative is part of an ideological movement led by the educated that is assertive and ground in post-colonialist theory. Accordingly, it was critical of the techniques and mechanisms of oppression as well as sought to attack the Zionist ideological foundations and to reveal its racist operations and the regimes that have preserved it so efficiently for many years. The uniqueness of this narrative is the intellectual offensive that continues to be advanced and, in parallel, development of the discourse struggle in Israel concerning the justification for Zionism and the concrete political proposal that Jews reject the taken-for-granted status of it as an ideology. This new narrative recognizes the historic difficulties of subversion as an emancipatory and, principally, moral effort. In addition, the new Mizrahi narrative shares the foundations and narrative of Palestinian victimization. In its radical version, the new Mizrahi narrative seeks to connect to the Palestinian narrative in order to create a new space here. According to this version, this action will take place gradually. The first stage will be characterized by opposition to Western European, Ashkenazic Zionism. The Eurocentric Zionism will surrender in the second stage, to be followed in the last stage by creation of a coalition of Jews and Arabs that will be establish through concrete actualization of the refugee status and victimization that is shared by both Palestinians and Mizrahim (whether as Mizrahim or Jewish-Arab). Not a speculative academic exercise, the goal sought by this narrative is delineate and to achieve a multicultural model in which equality, liberty, and social justice will overcome the nationalism and colonialism of either side; that is it will be neither Zionist nor Jewish. Thus, this approach stresses what is shared (e.g., acceptance of the Arab space and not a rejection of it; the legitimacy of the Arab language and culture). This is part of detachment from and historic judgment of the colonialist Zionist enterprise. This possibility includes moral elements that remove the evil and harm caused by Zionism for many years as well as inner cleansing – primarily among Ashkenazim – of attitudes towards Jews and non-Jews. Though, in this regard, it should be noted that, to date, the new narrative has not made similar claims that Palestinians undergo a similar process. The assumption seems to be that this should be tested, that the coalition proposed is a possibility that will be recognized by the Palestinians, and that they are prepared to undergo a similar, shared moral process that involves negating the state of Israel as a Jewish, Western state, a state of the Jewish people, and not only for those who live within it. These Mizrahi thinkers conducted a significant move through deconstruction and substitution of the Eurocentric narrative with a multi-cultural proposal that is optimistic and even attractively naïve. Today, they acknowledge that they did not take into account Palestinian nationalist violence directed to citizens, the traditionalist alternative, and widespread opposition within the Mizrahi community toward what is perceived to be Mizrahi seclusion. They also did not take into account the harsh criticism rendered by young and educated Mizrahim who claim that they were born into a complex, multi-dimensional, multi-layered identity that includes internalization of the language of the West and rules of the game of this complex identity. And, though they are critical of some of its values, this makes it difficult to mount internal emotional opposition to the West and to the globalization contained within this world. Hence, this more familiar world is preferred over the values of the Mizrahi-Arab alternative, particularly in regard to problems in the domains of democratic citizenship, stance taken toward women, and freedom of speech. Further, educated Mizrachim reject the post-colonialist perspective and are stridently critical of its dichotomization. They claim that such a division is irrelevant in a world in which older ideologies have collapsed and new spheres – such as cyberspace and others – are open to them in which they can present themselves with an Israeli identity that is not categorized as necessarily Mizrahi. (shrink)

We develop a timeout extension of propositional linear temporal logic to specify timing properties of timeout-based models of real-time systems. A timeout is used to model the execution of an action marking the end of a delay. With a view to expressing such timeout constraints, ToLTL uses a dynamic variable to abstract the timeout behaviour in addition to a variable which captures the global clock and some static timing variables which record time instances when discrete events occur. We (...) propose a corresponding timeout tableau for satisfiability checking of the ToLTL formulas. Further we prove that the validity checking for such an extended logic remains PSPACE-complete. Under discrete time semantics, with bounded timeout increments, the model-checking problem which verifies if a ToLTL-formula holds in a timeout Kripke structure is also shown to be PSPACE complete. We further prove that ToLTL, when interpreted over discrete time, can be embedded in the monadic second-order logic with.. (shrink)

In this paper, constructions of free algebras corresponding to multiplicative classical linear logic, its affine variant, and their extensions with -contraction () are given. As an application, the cardinality problem of some one-variable linear fragments with -contraction is solved.

This paper discusses how an understanding of Jung's psychological types is important for the relevance of Gilbert's multi-modal argumentation theory. Moreover, it highlights how the types have been confirmed by contemporary neuroscience and cognitive psychology. Based on Gilbert's approach, I extend multi-modal argumentation to the area of legal argumentation. It seems that when we leave behind the traditional fortress of “logical” legal argumentation, we "discover" alternate modes that have always been present, concealed in the theoretically underestimated rhetorical skills (...) of arguers. (shrink)

Separated and immediate extensions of valued fields. The notion of separated extension of valued fields was introduced by Baur. He showed that extensions of maximal fields are separated. We prove that, when (K, v) is Henselian with residual characteristic 0, then $(K, v) \subset (L, w)$ is separated iff L is linearly disjoint over K from each immediate extension of K.

The ‘causal-constitution’ fallacy, the ‘cognitive bloat’ worry, and the persisting theoretical confusion about the fundamental difference between the hypotheses of embedded (HEMC) and extended (HEC) cognition are three interrelated worries, whose common point—and the problem they accentuate—is the lack of a principled criterion of constitution. Attempting to address the ‘causal-constitution’ fallacy, mathematically oriented philosophers of mind have previously suggested that the presence of non-linear relations between the inner and the outer contributions is sufficient for cognitive extension. The abstract (...) idea of non-linearity, however, can be easily misunderstood and has, in the past, led to incorrect and counterintuitive conclusions about what may count as part of one’s overall cognitive system. In order to prevent any further mistakes I revisit dynamical systems theory to study the nature of the continuous mutual interactions that give rise to the aforementioned non-linear relations. Moreover, focusing on these interactions will allow us to provide two distinct arguments in support of the ontological postulation of extended cognitive systems, as well as an objective criterion of constitution. Accordingly, I put forward a version of HEC that treats continuous mutual interactions (and the resultant non-linear relations) not just as sufficient but also as necessary for cognitive extension. Such a qualified version of HEC may exclude certain alleged cases of cognitive extension where the agent does not mutually interact with his artifacts (e.g., shopping lists and directory services), but it is immune both to the ‘causal-constitution’ fallacy and the ‘cognitive bloat’ worry, and it can be sharply distinguished from HEMC. (shrink)

The papers in this volume are extended versions of presentations at the fourth International Workshop on Extensions of Logic Programming, held at the University of St Andrews, March/April 1993. Among the topics covered in the volume are: defintional reflection and completion, modules in lambda-Prolog, representation of logics as partial inductive definitions, non-procedural logic programming, knowledge representation, contradiction avoidance, disjunctive databases, strong negation, linear logic programming, proof theory and regular search spaces, finite sets and constraint logic programming, search-space pruning and (...) universal algebra, and implementation on transputer networks. (shrink)

We enrich intuitionistic logic with a lax modal operator and define a corresponding intensional enrichment of Kripke models M = (W, , V) by a function T giving an effort measure T(w, u) {} for each -related pair (w, u). We show that embodies the abstraction involved in passing from true up to bounded effort to true outright. We then introduce a refined notion of intensional validity M |= p : and present a corresponding intensional calculus iLC-h which gives a (...) natural extension by lax modality of the well-known G: odel/Dummett logic LC of (finite) linear Kripke models. Our main results are that for finite linear intensional models L the intensional theory iTh(L) = {p : | L |= p : } characterises L and that iLC-h generates complete information about iTh(L).Our paper thus shows that the quantitative intensional information contained in the effort measure T can be abstracted away by the use of and completely recovered by a suitable semantic interpretation of proofs. (shrink)

The logics considered here are the propositional Linear Logic and propositional Intuitionistic Linear Logic extended by a knotted structural rule: γ, xn → y / γ, xm → y. It is proved that the class of algebraic models for such a logic has the finite embeddability property, meaning that every finite partial subalgebra of an algebra in the class can be embedded into a finite full algebra in the class. It follows that each such logic has the finite (...) model property with respect to its algebraic semantics and hence that the logic is decidable. (shrink)

In this paper, we generalize the soft set to the hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

In this note we show: Let R = 〈R, <, +, 0, …〉 be a semi-bounded o-minimal expansion of an ordered group, and G a group definable in R of linear dimension m . Then G is a definable extension of a bounded definable group B by 〈Rm, +〉.

We propose a new, rather simple and short proof of Kripke-completeness for the predicate variant of Dummett's logic. Also a family of Kripke-incomplete extensions of this logic that are complete w.r.t. Kripke frames with equality (or equivalently, w.r.t. Kripke sheaves [8]), is described.

The paper aims at providing the multi-modal propositional logic LTK with a sound and complete axiomatisation. This logic combines temporal and epistemic operators and focuses on m odeling the behaviour of a set of agents operating in a system on the background of a temporal framework. Time is represented as linear and discrete, whereas knowledge is modeled as an S5-like modality. A further modal operator intended to represent environment knowledge is added to the system in order to achieve (...) the expressive power sufficient to describe the piece of information available to the agents at each moment in the flow of time. (shrink)

Given a theoryTextending that of dense linear orders without endpoints, in a language ℒ ⊇ {<}, we are interested in extensionsT′ ofTin languages extending ℒ by unary relation symbols that are each interpreted in models ofT′ as sets that are both dense and codense in the underlying sets of the models.There is a canonically “wild” example, namelyT= Th andT′ = Th. Recall thatTis o-minimal, and so every open set definable in any model ofThas only finitely many definably connected components. (...) But it is well known that 〈ℝ, <, +, · ℚ 〉 defines every real Borel set, in particular, every open subset of any finite cartesian power of ℝ and every subset of any finite cartesian power of ℚ. To put this another way, the definable open sets in models ofTare essentially as simple as possible, whileT′ has a model where the definable open sets are as complicated as possible, as is the structure induced on the new predicate.In contrast to the preceding example, if ℝalgis the set of real algebraic numbers andT′ Th, then no model ofT′ defines any open set that is not definable in the underlying model ofT. (shrink)

Investment in agricultural extension, as well as its design and practice, are usually based on the assumption that agricultural science generates technology (“applied science“), which extension experts transfer to “users“. This model negates local knowledge and creativity, ignores farmers' self-confidence and social energy as important sources of change, and, in its most linear expression, does not pay attention to information from and about farmers as a condition for anticipating utilization.In practice, farmers rely on knowledge developed by farmers, (...) reinvent ideas brought from outside and actively integrate them into complex farming decisions. Effective extension seems based on checks and balances that match intervention power with farmers' countervailing power, and mobilize farmers' creativity and participation in technology development and exchange.Alternative models for informing extension investment, design, and practice stress adult learning and its facilitation. The farmer is seen as an expert and farm development as driven by farmers' energy and communication. The article is a case study of a rare large scale attempt to use such an alternative model. It suggests that a shift to knowledgeintensive sustainable practices requires a learning process based on participation and empowerment. (shrink)

ABSTRACTWith over 560 citations reported on Google Scholar by April 2018, a publication by Juslin and Gabrielsson presented evidence supporting performers’ abilities to communicate, with hig...

A critical re-examination of the history of the concepts of space (including spacetime of general relativity and relativistic quantum field theory) reveals a basic ontological elusiveness of spatial extension, while, at the same time, highlighting the fact that its epistemic primacy seems to be unavoidably imposed on us (as stated by A.Einstein “giving up the extensional continuum … is like to breathe in airless space”). On the other hand, Planck’s discovery of the atomization of action leads to the fundamental (...) recognition of an ontology of non-spatial, abstract entities (Quine) for the quantum level of reality (QT), as distinguished from the necessarily spatio-temporal, experimental revelations (measurements). The elementary quantum act (measured by Planck’s constant) has neither duration nor extension, and any genuinely quantum process literally does not belong in the Raum and time of our experience. As Heisenberg stresses: “Während also die klassische Physik ein objectives Geschehen in Raum and Zeit zum Gegenstand hat, für dessen Existenz seine Beobachtung völlig irrelevant war, behandelt die Quantentheorie Vorgänge, die sozusagen nur in den Momenten der Beobachtung als raumzeitliche Phänomene aufleuchten, und über die in der zwischenzeit anschaulische physikalische Aussagen sinloss sind”. An admittedly speculative, hazardous conjecture is then advanced concerning the relation of such quantum ontology with the role of the pre-phenomenal continuum (Husserl) in the perception of macroscopically distinguishable objects in the Raum and time of our experience. Although rather venturesome, it brings together important philosophical issues. Coherently with recent general results in works on the foundations of QT, it is assumed that the linearity of quantum dynamical evolution does not apply to the central nervous system of living beings at a certain level of the evolutionary ramification and at the pre-conscious stage of subjectivity. Accordingly, corresponding to the onset of a non-linear dynamic evolution, a ‘primary spatial’ reduction is ‘continually’ taking place, thereby constituting the neural precondition for the experience of distinguishable macroscopic objects in the continuous spatial extension. While preventing the theoretically possible quantum superpositions of macroscopic objects from being perceivable by living beings, the ‘primary reduction’ has no effect on the standard processes concerning quantum level entities involved in laboratory man-made experiments. In this connection, an experimental check which might falsify the conjecture is briefly discussed. The approach suggested here, if sound, leads to a naturalization of that part of Kant’s Transcendental Aesthetics than can survive the Euclidean catastrophe. According to such naturalized transcendentalism, “space can well be transcendental without the axioms being so”, in agreement with a well-known statement by Boltzman. Finally, as far as QT is concerned, the conjecture entails that a scheme for quantum measurement of the von Neumann type cannot even ‘leave the ground’, vindicating Bohr’s viewpoint. A quantum theory of measurement, in a proper sense, turns out to be unnecessary and in fact impossible. (shrink)

We prove a generalization of Maehara’s lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig’s interpolation property. As a corollary, we obtain a direct proof of interpolation for (classical and intuitionistic) first-order logic with identity, as well as interpolation for several mathematical theories, including the theory of equivalence relations, (strict) partial and linear orders, and various intuitionistic order theories such as apartness and positive (...) partial and linear orders. (shrink)

In this paper, we generalize the definition of Neutrosophic sets and present a method for extending crisp functions on Neutrosophic sets and study some properties of such extended functions.

The appearance of nonlinear equations in science, engineering, economics, and medicine cannot be denied. Solving such equations requires numerical methods having higher-order convergence with cost-effectiveness, for the equations do not have exact solutions. In the pursuit of efficient numerical methods, an attempt is made to devise a modified strategy for approximating the solution of nonlinear models in either scalar or vector versions. Two numerical methods of second-and sixth-order convergence are carefully merged to obtain a hybrid multi-step numerical method with (...) twelfth-order convergence while using seven function evaluations per iteration, resulting in the efficiency index of about 1.4262. The convergence is also ascertained theoretically, and the asymptotic error constant is computed. Furthermore, various numerical methods of varying orders are used to compare the numerical results obtained with the proposed hybrid method in approximate solution, number of iterations, absolute error, absolute functional value, and the machine time measured in seconds. The obtained results outperformed the chosen methods when applied models arising from physical and natural fields were solved. Finally, to observe the convergence graphically, some complex polynomials are plotted as polynomiographs, wherein the rapid convergence of the proposed method is guaranteed. (shrink)

In this paper the following theorem is proved regarding groups of finite Morley rank which are perfect central extensions of quasisimple algebraic groups.Theorem1.Let G be a perfect group of finite Morley rank and let C0be a definable central subgroup of G such that G/C0is a universal linear algebraic group over an algebraically closed field; that is G is a perfect central extension of finite Morley rank of a universal linear algebraic group. Then C0= 1.Contrary to an impression (...) which exists in some circles, the center of the universal extension of a simple algebraic group, as an abstract group, is not finite in general. Thus the finite Morley rank assumption cannot be omitted.Corollary1.Let G be a perfect group of finite Morley rank such that G/Z(G) is a quasisimple algebraic group. Then G is an algebraic group. In particular, Z(G) is finite([4],Section27.5).An understanding of central extensions of quasisimple linear algebraic groups which are groups of finite Morley rank is necessary for the classification oftamesimpleK*-groupsof finite Morley rank, which constitutes an approach to the Cherlin-Zil’ber conjecture. For this reason the theorem above and its corollary were proven in [1] (Theorems 4.1 and 4.2) under the assumption oftameness, which simplifies the argument considerably. The result of the present paper shows that this assumption can be dropped. The main line of argument is parallel to that in [1]; the absence of the tameness assumption will be countered by a model-theoretic result and results fromK-theory. The model-theoretic result places limitations on definability in stable fields, and may possibly be relevant to eliminating certain other uses of tameness. (shrink)

In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes (parameters)’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and for a more (...) exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined be-tween each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life. (shrink)

This paper proposes a semantic description of the linear step-like temporal multi-agent logic with the universal modality $\mathcal{LTK}.sl_U$ based on the idea of non-reflexive non-transitive nature of time. We proved a finite model property and projective unification for this logic.

ABSTRACT:Although the literature on multi-stakeholder initiatives for sustainability has grown in recent years, it is scattered across several academic fields, making it hard to ascertain how individual disciplines, such as business ethics, can further contribute to the debate. Based on an extensive review of the literature on certification and principle-based MSIs for sustainability, we show that the scholarly debate rests on three broad themes : theinputinto creating and governing MSIs; theinstitutionalizationof MSIs; and theimpactthat relevant initiatives create. While our discussion (...) reveals the theoretical underpinnings of the 3Is, it also shows that a number of research challenges related to business ethics remain unaddressed. We unpack these challenges and suggest how scholars can utilize theoretical insights in business ethics to push the boundaries of the field. Finally, we also discuss what business ethics research can gain from theory development in the MSI field. (shrink)

The monoidal t-norm based logic MTL is obtained from Hájek''s Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational (...) completeness (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics. (shrink)

Collaborative consumption is proposed as a potential step beyond unsustainable linear consumption patterns toward more sustainable consumption practices. Despite mounting interest in the topic, little is known about the determinants of this consumer behavior. We use an extended theory of planned behavior to examine the relative influence of consumers’ personal norms and the theory’s basic sociopsychological variables attitudes, subjective norms, and perceived behavioral control on collaborative consumption. Moreover, we use this framework to examine consumers’ underlying value and belief structure (...) regarding collaborative consumption. We measure these aspects for 224 consumers in a survey and then assess their self-reported collaborative consumption behavior in a second survey. Our structural model fits the data well. Collaborative consumption is more strongly—through intentions—influenced by personal norms and attitudes than by subjective norms. Personal norms to consume collaboratively are determined by consumers’ altruistic, biospheric, and egoistic value orientations. Cost savings, efficient use of resources, and community with others are found to be consumers’ attitudinal beliefs underlying collaborative consumption. We conclude that collaborative consumption can be pin-pointed neither as a mere form of economic exchange nor as a primarily normative form of sharing resources. Instead, collaborative consumption is determined by economic/egoistic (e.g., cost savings) and normative (e.g., altruistic and biospheric value orientations) motives. Implications for collaborative consumption research, the theory of planned behavior, and practitioners are discussed. (shrink)

In this paper, we investigate the expressiveness of the variety of propositional interval neighborhood logics , we establish their decidability on linearly ordered domains and some important subclasses, and we prove the undecidability of a number of extensions of PNL with additional modalities over interval relations. All together, we show that PNL form a quite expressive and nearly maximal decidable fragment of Halpern–Shoham’s interval logic HS.

We introduce a linear analogue of Läuchli's semantics for intuitionistic logic. In fact, our result is a strengthening of Läuchli's work to the level of proofs, rather than provability. This is obtained by considering continuous actions of the additive group of integers on a category of topological vector spaces. The semantics, based on functorial polymorphism, consists of dinatural transformations which are equivariant with respect to all such actions. Such dinatural transformations are called uniform. To any sequent in Multiplicative (...) class='Hi'>Linear Logic , we associate a vector space of“diadditive” uniform transformations. We then show that this space is generated by denotations of cut-free proofs of the sequent in the theory MLL + MIX. Thus we obtain a full completeness theorem in the sense of Abramsky and Jagadeesan, although our result differs from theirs in the use of dinatural transformations.As corollaries, we show that these dinatural transformations compose, and obtain a conservativity result: diadditive dinatural transformations which are uniform with respect to actions of the additive group of integers are also uniform with respect to the actions of arbitrary cocommutative Hopf algebras. Finally, we discuss several possible extensions of this work to noncommutative logic.It is well known that the intuitionistic version of Läuchli's semantics is a special case of the theory of logical relations, due to Plotkin and Statman. Thus, our work can also be viewed as a first step towards developing a theory of logical relations for linear logic and concurrency. (shrink)

We suggest that, far from establishing an inconsistency in the standard theory of the geometrical linear continuum, Zeno’s Paradox of Extension merely establishes an inconsistency between the standard theory of geometrical magnitude and a misguided system of length measurement. We further suggest that our resolution of Zeno’s paradox is superior to Adolf Grünbaum’s now standard resolution based on Lebesgue measure theory.

This paper is concerned with the problem of extending an antisymmetric binary relation on a set to a linear order on the power set. A necessary and sufficient condition is offered.

In the paper we obtain a new characterization of the BCK-algebras which are subdirect product of BCK-chains. We give an axiomatic algebraizable extension of the BCK-calculus, by means of a recursively enumerable set of axioms, such that its equivalent algebraic semantics is definitionally equivalent to the quasivariety of BCK-algebras generated by the BCK-chains. We propose the concept of "linearization of a system" and we give some examples.