The purpose of this paper is to introduce a bi-intuitionistic sequent calculus and to give proofs of admissibility for its structural rules. The calculus I will present, called SC2Int, is a sequent calculus for the bi-intuitionistic logic 2Int, which Wansing presents in [2016a]. There he also gives a natural deduction system for this logic, N2Int, to which SC2Int is equivalent in terms of what is derivable. What is important is that these calculi represent a kind of bilateralist reasoning, (...) since they do not only internalize processes of verifcation or provability but also the dual processes in terms of falsifcation or what is called dual provability. In [Wansing, 2017] a normal form theorem for N2Int is stated, here, I want to prove a cut-elimination theorem for SC2Int, i.e., if successful, this would extend the results existing so far. (shrink)

1. A. Heyting (1930) introduced an intermediate logic whose semantics is based on a pair of states (‘here’ and ‘there’). This logic was axiomatized by Hosoi (1966), using the sequence of intermedia...

This article discusses Abū Isḥāq al-Naẓẓām’s (d. 231/845) (one of the first Muʽtazilī thinkers); understanding of Allah-world relationship, his theory of nature (tab‘) and his view on miracles. In a proposal form, Muʽtazilī scholars accept that the miracle, which is the actual confirmation, must occur, since it is not possible for Allah to confirm His messenger (prophet) in a way that everyone can hear and in a direct word. Since the Prophet's message can be authenticated only by a miracle, Muʽtazilī (...) thinkers paid great attention to this issue, organized and formed natural theories about the universe in a way that miracles can occur. Naẓẓām explains a kind of miracle that occurs under the power of Allah, by his theory of nature called latency and occurrence (kumūn-ẓuhūr). His view of miracles is rooted in the Muʽtazilī classification of miracles. Naẓẓām argues that in the theory of nature, things are infinitely divided. He also argues that all qualities considered accident (aʽrāḍ) by other Muslim theologians are different objects as only motion and rest are the only accidents. According to him, the universe consists of objects and accidents of motion only. In each object in the universe, an unlimited number of opposing objects (sub-components) that have different effects on each other is located in the same space. Those objects in the same space are intervened (tadākhul) with each other. Kumūn refers to sub-components that are located inside the object in a state of passing into each other, and a state of balancing each other through the push-pull motion (i‘timād). Ẓuhūr is an outward movement of the sub-component from where it is located when an impact imposed outside the object interacts with one of the sub-components contained in it. Naẓẓām says that too many opposing sub-components, such as heaviness-lightness, heat-coldness contained in the object, form an internal dynamic by providing balancing each other through inside the object with the push-pull motion. The state of balance inside the object is disrupted by an external factor affecting one of the sub-components. An external thing approaching the object interacts with one of the sub-components contained in the object. Then, the affected sub-component moves out of the object and thus the state of balance inside the object is disrupted. According to the theory of kumūn-ẓuhūr, change in objects occurs when the balance within the object is disturbed. The change in the balance also occurs not by the direct intervention of Allah and the creation of accidents, but by the disruption in the balance of natures within the object. Naẓẓām, who advocates the intrinsic natures in things, has been criticized for not leaving any room for Allah’s influence on objects at least through miracles. This criticism is not correct. Naẓẓām says that the nature of objects depends on God, and it is possible for God to intervene in them at any time. According to him, Allah can force opposing objects into a union that is not in their natures. In their natures, unification can separate those by applying pull and push. In this way, Naẓẓām sees the intervention of Allah as possible in the occurrence of a situation that is the opposite of what is present in the nature of objects. In Naẓẓām's theory of kumūn-ẓuhūr, there are suppressed natures and sub-components that are in a weak state inside the actual object. Furthermore, they cannot go out in any way from the actual object. One of these suppressed natures found in the object is removed from the nature of the object by the intervention of Allah when a miracle occurs in the hands of theProphet. In this case, the miracle is not something new that Allah has created, but that Allah has disclosed a hidden sub-component that is hidden in that thing that has never appeared before. Naẓẓām’s view of miracle is something occurring under the power of the created, which Muʽtazilī scholars accept in the classification of miracles in relation to, the theory of sarfa. He suggests that the Qur'an, which he accepts under the power of the created, would not be a miracle, if the Arabs could dispute it. However, according to him, the Qur'an is a miracle because Allah prevents them from the dispute. In his understanding of sarfa, the miracles occur directly as an act of God’s divine intervention with human beings. This study investigates Naẓẓām’s view of miracles along with his theory of nature and his understanding of sarfa. (shrink)

This article discusses Abū ʽUthmān al-Jāḥiẓ (d. 255/869) (one of the first Muʽtazilī scholars) Allah-world relationship, his understanding of custom, and his view on miracles. The Muʻtazilī thinkers examined the problem of miracles within their concept of prophethood. They divide miracles, which they accept as the only proof of prophethood, into two: those under the power of Allah and under the power of the created. Jāḥiẓ explains these two sorts of miracles with the order in the universe established by Allah (...) and people and expresses this order with the concept of custom (ʻāda). Jāḥiẓ divides custom into three. The first of these is the “qā’im (constant) custom”, which is based on the theory of kumūn-ẓuhūr and expresses the general rules that occur as a requirement of the general functioning in the universe. According to Jāḥiẓ “qā’im (constant) custom” is that knowledgeable people are aware of the custom of the universe. This custom is an order created by Allah in the eyes of intelligent and knowledgeable people, which is continuous and therefore cannot be interrupted, and in which there is no chaos. He states that this order is realized through the natures in the objects, which are knowable to everyone. But rarely a nature in this order can be interrupted due to a situation that takes it out of the natural flow and cannot be explained by natural causes. According to him, this is proof that nature, which has the defining feature of the object, is created by the creator, and maintains its continuity based on an arranged program. However, the creator can involve in this order when necessary. In this type of custom, God’s intervention occurs by breaking the qā’im custom that continues on a regular basis. The second of these is the “regional custom”, which is not known to everyone but only known to people living in a certain area. Jāḥiẓ states that the miracle in this type of custom occurred when Allah broke the custom known to the people in the region. The third of these is “social custom” which is established by people. For Jāḥiẓ, the miracles of this kind are under the power of people. He argues that the miracle in this type of custom occurs with sarfa, that is, by God’s intervention with human’s motive or knowledge. In this study, Jāḥiẓ’s view of miracles is discussed together with his theory of nature, his understanding of custom and sarfa. (shrink)

Epistemology and epistemic logic At first sight, the modern agenda of epistemology has little to do with logic. Topics include different definitions of knowledge, its basic formal properties, debates between externalist and internalist positions, and above all: perennial encounters with sceptics lurking behind every street corner, especially in the US. The entry 'Epistemology' in the Routledge Encyclopedia of Philosophy (Klein 1993) and the anthology (Kim and Sosa 2000) give an up-to-date impression of the field. Now, epistemic logic (...) started as a contribution to epistemology, or at least a tool in its modus operandi, with the seminal book Knowledge and Belief (Hintikka's 1962, 2005). Formulas like Ki for "the agent i knows that " Bi for "the agent i believes that " provided logical forms for stating and analyzing philosophical propositions and arguments. And more than that, their model-theoretic semantics in terms of ranges of alternatives provided an appealing extensional way of thinking about what agents know or believe in a given situation. In particular, on Hintikka's view, an agent knows those propositions which are true in all situations compatible with what she knows about the actual world; i.e., her current range of uncertainty. (shrink)

Hegel oneself indicate “essential theory " Thereunto category transition, large orientation yes as best as one can in accord with cognize course process of, to this aspect ought earnest comprehend, but history with logicality improbable Absolute coherent, More Plus For the sake of fabricate institutions of demand, additionally have to pray in aid of imaginary, To this aspect ought to appropriate comment critically, though never be able to use dot supplant bodily general denial.

Hegel oneself indicate “essential theory " Thereunto category transition, large orientation yes as best as one can in accord with cognize course process of, to this aspect ought earnest comprehend, but history with logicality improbable Absolute coherent, More Plus For the sake of fabricate institutions of demand, additionally have to pray in aid of imaginary, To this aspect ought to appropriate comment critically, though never be able to use dot supplant bodily general denial.

Hegel oneself indicate “essential theory " Thereunto category transition, large orientation yes as best as one can in accord with cognize course process of, to this aspect ought earnest comprehend, but history with logicality improbable Absolute coherent, More Plus For the sake of fabricate institutions of demand, additionally have to pray in aid of imaginary, To this aspect ought to appropriate comment critically, though never be able to use dot supplant bodily general denial.

Emotion recognition is an important part of building an intelligent human-computer interaction system and plays an important role in human-computer interaction. Often, people express their feelings through a variety of symbols, such as words and facial expressions. A business ecosystem is an economic community based on interacting organizations and individuals. Over time, they develop their capabilities and roles together and tend to develop themselves in the direction of one or more central enterprises. This paper aims to study a multimodal ER (...) method based on attention mechanism. It analyzes the current emotional state of consumers and the development direction of enterprises through multi-modal ER of human emotions and analysis of market trends, so as to provide the most appropriate response or plan. This paper firstly describes the related methods of multimodal ER and deep learning in detail, and briefly outlines the meaning of enterprise strategy in the business ecosystem. Then, two datasets, CMU-MOSI and CMU-MOSEI, are selected to design the scheme for multimodal ER based on self-attention mechanism. Through the comparative analysis of the accuracy of single-modal and multi-modal ER, the self-attention mechanism is applied in the experiment. The experimental results show that the average recognition accuracy of happy under multimodal ER reaches 91.5%. (shrink)

v. 1. al-Nuṣūṣ al-manṭiqīyah -- v. 2. al-Shurūḥ al-manṭiqīyah -- al-mujallad 3. al-Shurūḥ ʻalá al-nuṣūṣ al-manṭiqīyah.

Mindfulness and accordant interventions are often used as complementary treatments to psychological or psychosomatic problems. This has also been gradually integrated into daily lives for the promotion of psychological well-being in non-clinical populations. The experience of mindful acceptance in a non-judgmental way brought about the state, which was less interfered by a negative effect. Mindfulness practice often begins with focused attention meditation restricted to an inner experience. We postulate that the brain areas related to an interoceptive function would demonstrate (...) an intrinsic functional change after mindfulness training for the mindful novices along with paying more attention to internal processes. To further explore the influence of mindfulness on the organization of the brain regions, both functional connectivity in the voxel and the region of interest level were calculated. In the current study, 32 healthy volunteers, without any meditation experiences, were enrolled and randomly assigned to a mindfulness-based stress reduction group or control group. Participants in the MBSR group completed 8 weeks of mindfulness-based stress reduction and rated their mindfulness skills before and after MBSR. All subjects were evaluated via resting-state functional MRI in both baselines and after 8 weeks. They also completed a self-report measure of their state and trait anxiety as well as a positive and negative affect. Pre- and post-MBSR assessments revealed a decreased amplitude of low-frequency fluctuations in the right anterior cingulate gyrus, left anterior and posterior insula, as well as left superior medial frontal gyrus in MBSR practitioners. Strengthened FC between right anterior cingulate cortex and aIC.R was observed. The mean ALFF values of those regions were inversely and positively linked to newly acquired mindful abilities. Along with a decreased negative affect score, our results suggest that the brain regions related to attention and interoceptive function were involved at the beginning of mindfulness. This study provides new clues in elucidating the time of evaluating the brain mechanisms of mindfulness novices. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Diacritics 29.4 (1999) 84-115 [Access article in PDF] Be-longing and Bi-lingual States Doris Sommer "How sad that people don't keep commitments any more. Even marriages last only about five years.""Yes, but long-distance marriages can stretch those five years out over weekends and vacations to make relationships last a lifetime."Benedict Anderson's provocative new book, The Spectre of Comparisons: Nationalism, Southeast Asia and the World, raises questions about political relationships over (...) time and over space. Like precarious modern marriages and their corollary "political" kinships (in-laws in Spanish are one's familia política), national sentiment today strains with the movements of transnational communities from home to distant enclaves. Over time, ties can unravel as modern subjects choose, or not, to identify with adopted political relatives. Is one's country the bastion of a people reluctant to receive more immigrants? Is it the sender of surplus people who will, in turn, send money home? (Heads of state in El Salvador, Guatemala, and Mexico typically object to US restrictions on immigration.) Or is it the harbor for many peoples? Does belonging even to a recently invented country anchor an existential need, a be-longing, because being a "man"--as Hannah Arendt still called the subject of politics--means striving for recognition among equals? Or, do many citizens today feel like resident aliens (to themselves or to others), belonging rather to ethnic minorities and perhaps--long-distance--to other nations of origin or of choice? Anderson is right to worry about precarious belongings and optional obligations.In the end though, he finds solace from the threats of egotism and despair, and from the social decomposition of too much movement (what Arjun Appadurai calls "modernity at large") in the resilient promise of the "goodness of nations." Confidence in the extrapersonal goals and pride in national belonging appears, almost miraculously, in the last of seventeen chapters. Each of these brilliant and erudite essays will reconfirm our admiration for Anderson. My own personal debt includes his extraordinary generosity and the good counsel that encourages me to follow him, sometimes with a swerve, as will be evident when my appreciation for be-longing plays bi-lingual games.The opening pages of The Spectre of Comparisons theorize a paradox in the postcolonial condition: the inescapable folly of comparing one's nation to another, or to a mother country. Concepts like nation or culture, after all, take on meaning in their particular contexts and by contrast with others. The core chapters chronicle aborted beginnings and abusive conflations of the nation and the state. But hope has the last word, thanks to three guarantees of national imaginings: the promising and innocent unborn generations; the nation's dead (war heroes); and the living who are ever willing to give the nation another chance, and yet another. Feelings of pride and shame come together in the end, because citizens invest, often against the evidence, in "the goodness [End Page 84] of nations" [364]. This resilience shows up right after the trouble in chapter 16, where shame was the connection between nation and narrator in Mario Vargas Llosa's 1987 novel about Peru. Unfounded but unrelenting, Anderson's hope follows on shame rather abruptly and suggests that shame itself is a sign of our care for our countries. 1 The narrator of El hablador had tried to escape from his ill-fated country, his "malhadado país," only to be haunted by it.My question is whether Anderson's coda to this Peruvian novel is inspired by the same indomitable demon of comparisons that he has been exposing throughout the essays. José Rizal had named the meddling devil to blame it for distracting the Filipino from the lovely garden he saw in Manila, assailing him with memories of a European original or model [2]. This double vision raises a specter of possible inauthenticity; it undermines meaning as models slip from centers to peripheries. Local concepts lose their particularities in global vocabularies. Anderson calls the movement a "logic of seriality." I prefer to call it trans-latio, literally a carrying from one place to another... (shrink)

In Belnap's useful 4-valued logic, the set 2 = {T, F} of classical truth values is generalized to the set 4 = ������(2) = {Ø, {T}, {F}, {T, F}}. In the present paper, we argue in favor of extending this process to the set 16 = ᵍ (4) (and beyond). It turns out that this generalization is well-motivated and leads from the bilattice FOUR₂ with an information and a truth-and-falsity ordering to another algebraic structure, namely the trilattice SIXTEEN₃ with (...) an information ordering together with a truth ordering and a (distinct) falsity ordering. Interestingly, the logics generated separately by the algebraic operations under the truth order and under the falsity order in SIXTEEN₃ coincide with the logic of FOUR₂, namely first degree entailment. This observation may be taken as a further indication of the significance of first degree entailment. In the present setting, however, it becomes rather natural to consider also logical systems in the language obtained by combining the vocabulary of the logic of the truth order and the falsity order. We semantically define the logics of the two orderings in the extended language and in both cases axiomatize a certain fragment comprising three unary operations: a negation, an involution, and their combination. We also suggest two other definitions of logics in the full language, including a bi-consequence system. In other words, in addition to presenting first degree entailment as a useful 16-valued logic, we define further useful 16-valued logics for reasoning about truth and (non-)falsity. We expect these logics to be an interesting and useful instrument in information processing, especially when we deal with a net of hierarchically interconnected computers. We also briefly discuss Arieli's and Avron's notion of a logical bilattice and state a number of open problems for future research. (shrink)

This book constitutes the strictly refereed post-workshop proceedings of the 11th International Workshop on Computer Science Logic, CSL '97, held as the 1997 Annual Conference of the European Association on Computer Science Logic, EACSL, in Aarhus, Denmark, in August 1997. The volume presents 26 revised full papers selected after two rounds of refereeing from initially 92 submissions; also included are four invited papers. The book addresses all current aspects of computer science logics and its applications and thus presents (...) the state of the art in the area. (shrink)

The paper begins with a more carefully stated version of ontologically neutral (ON) logic, originally introduced in (Hailperin, 1997). A non-infinitistic semantics which includes a definition of potential infinite validity follows. It is shown, without appeal to the actual infinite, that this notion provides a necessary and sufficient condition for provability in ON logic.

Classical logic is often characterized through certain laws such as bi-valence and sharpness of concepts, among others. My view is that its most fundamental feature is a commitment to an objective conception of truth, which goes together with a realistic metaphysical view. Truth is objective in that it derives from the nature of reality, and is not dependent on beliefs, theories, practices, and the like. Classical logic is a theory of logical properties, logical truths, and logical states of (...) affairs. (shrink)

In this paper, we introduce a new four-valued logic which may be viewed as a variation on the theme of Kubyshkina and Zaitsev's Logic of Rational Agent textbf{LRA} cite{LRA}. We call our logic $ bf LIRA$. In contrast to textbf{LRA}, it has three designated values instead of one and a different interpretation of truth values, the same as in Zaitsev and Shramko's bi-facial truth logic cite{ZS}. This logic may be useful in a situation when according (...) to an agent's point of view her/his reasoning is rational, while from the external one it might be not the case. One may use textbf{LIRA}, if one wants to reconstruct an agent's way of thinking, compare it with respect to the real state of affairs, and understand why an agent thought in this or that way. Moreover, we discuss Kubyshkina and Zaitsev's necessity and possibility operators for textbf{LRA} definable by means of four-valued Kripke-style semantics and show that, due to two negations of textbf{LRA}, two more possibility operators for textbf{LRA} can be defined. Then we slightly modify all these modalities to be appropriate for $bf LIRA$. Finally, we formalize all the truth-functional $ n $-ary extensions of the negation fragment of $bf LIRA$ as well as their basic modal extension via linear-type natural deduction systems. (shrink)

In this paper we present an extension of (bunched) separation logic, Boolean BI, with epistemic and dynamic epistemic modalities. This logic, called action model separation logic ( \(\mathrm {AMSL}\) ), can be seen as a generalization of public announcement separation logic in which we replace public announcements with action models. Then we not only model public information change (public announcements) but also non-public forms of information change, such as private announcements. In this context the semantics for (...) the connectives \(*\) and \(\mathrel {-*}\) from separation logic are epistemic versions of their usual semantics. This is because formulas are interpreted in states, not in resources, and agents may be uncertain between different states representing the same resource. We present the logic \(\mathrm {AMSL}\) and its semantics, with a detailed case study that highlights its interest for modeling. We also prove the elimination of the dynamics modalities and discuss some alternative epistemic semantics for the separation connectives. (shrink)

Let L be a quantum logic, here an orthoalgebra, and let Δ be a convex set of states on L. Then Δ generates a base-normed space, and the dual-order unit-normed space contains a canonically constructed homomorphic copy of L, denoted by eΔ(L). A convex set Δ of states on L is said to be ample provided that every state on L is obtained by restricting an element of the base of the bi-dual order unit-normed space to eΔ(L). For (...) a quantum logic L we show that a convex set of states Δ is ample if and only if Δ is weakly dense in the convex set of all states on L. The notion of ampleness is then discussed in the context of Gleason-type theorems for W* algebras and JBW algebras and also in the context of classical logics. (shrink)

Bi-intuitionistic logic is the result of adding the dual of intuitionistic implication to intuitionistic logic. In this note, we characterize the expressive power of this logic by showing that the first order formulas equivalent to translations of bi-intuitionistic propositional formulas are exactly those preserved under bi-intuitionistic directed bisimulations. The proof technique is originally due to Lindstrom and, in contrast to the most common proofs of this kind of result, it does not use the machinery of neither saturated (...) models nor elementary chains. (shrink)

The well-known algebraic semantics and topological semantics for intuitionistic logic (Int) is here extended to Wansing's bi-intuitionistic logic (2Int). The logic 2Int is also characterised by a quasi-twist structure semantics, which leads to an alternative topological characterisation of 2Int. Later, notions of Fregean negation and of unilateralisation are proposed. The logic 2Int is extended with a ‘Fregean negation’ connective ∼, obtaining 2Int∼, and it is showed that the logic N4⋆ (an extension of Nelson's paraconsistent (...) class='Hi'>logic) results to be the unilateralisation of 2Int∼ via ∼. The logic 2Int∼ is also characterised by a Kripke-style semantics, a twist structure semantics and a topological semantics. (shrink)

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting (...) to embeddings, semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants. (shrink)

We present a multiple-assumption multiple-conclusion system for bi-intuitionistic logic. Derivations in the systems are graphs whose edges are labelled by formulas and whose nodes are labelled by rules. We show how to embed both the standard intuitionistic and dual-intuitionistic natural deduction systems into the proposed system. Soundness and completeness are established using translations with more traditional sequent calculi for bi-intuitionistic logic.

Bi-intuitionistic logic is the union of intuitionistic and dual intuitionistic logic, and was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her subsequent ‘cut-free’ sequent calculus has recently been shown to fail cut-elimination. We present a new cut-free sequent calculus for bi-intuitionistic logic, and prove it sound and complete with respect to its Kripke semantics. Ensuring completeness is complicated by the interaction between intuitionistic implication and dual intuitionistic exclusion, similarly to future and (...) past modalities in tense logic. Our calculus handles this interaction using derivations and refutations as first class citizens. We employ extended sequents which pass information from premises to conclusions using variables instantiated at the leaves of refutations, and rules which compose certain refutations and derivations to form derivations. Automated deduction using terminating backward search is also possible, although this is not our main purpose. (shrink)

In this paper I shall argue that Tim Williamson’s argument for the anti-luminosity of many mental states faces difficult logical, psychological and epistemological problems. From a logical point of view, his argument is correct. However, the contrary argument that says that the anti-luminosity thesis does not necessarily follow from it is also correct. This opens a sceptical scenario. Hence, if Williamson wants to convince us that we should rationally prefer his argument rather than the other, he needs to add considerations (...) that are not merely logical. These are psychological and epistemological in nature. However, none of these considerations is convincing. (shrink)

We prove that certain natural sequent systems for bi-intuitionistic logic have the analytic cut property. In the process we show that the (global) subformula property implies the (local) analytic cut property, thereby demonstrating their equivalence. Applying a version of Maehara technique modified in several ways, we prove that bi-intuitionistic logic enjoys the classical Craig interpolation property and Maximova variable separation property; its Halldén completeness follows.

We propose a new sequent calculus for bi intuitionistic logic which sits somewhere between display calculi and traditional sequent calculi by using nested sequents. Our calculus enjoys a simple (purely syntactic) cut elimination proof as do display calculi. But it has an easily derivable variant calculus which is amenable to automated proof search as are (some) traditional sequent calculi. We first present the initial calculus and its cut elimination proof. We then present the derived calculus, and then present a (...) proof search strategy which allows it to be used for automated proof search. We prove that this search strategy is terminating and complete by showing how it can be used to mimic derivations obtained from an existing calculus GBiInt for bi intuitionistic logic. As far as we know, our new calculus is the first sequent calculus for bi intuitionistic logic which uses no semantic additions like labels, which has a purely syntactic cut elimination proof, and which can be used naturally for backwards proof search. Keywords: Bi-intuitionistic logic, display calculi, proof search. (shrink)

Review of the paper mentioned in the title.