We extend BDDs for plain propositional logic to the fragment of first order logic, consisting of quantifier free logic with zero, successor and equality. We allow equations with zero and successor in the nodes of a BDD, and call such objects -BDDs. We extend the notion of Ordered BDDs in the presence of zero, successor and equality. -BDDs can be transformed to equivalent Ordered -BDDs by applying a number of rewrite rules until a normal form is reached. All paths in (...) these ordered -BDDs represent satisfiable conjunctions. The major advantage of transforming a formula to an equivalent Ordered -BDD is that on the latter it can be observed in constant time whether the formula is a tautology, a contradiction, or just satisfiable. (shrink)

Don DeLillo’s White Noise depicts a world of rapid techno-scientific and economical changes. Paul Virilio’s concepts of dromology and speed, as well as his notions of accident and technology, seem to be the most relevant in order to examine a novel centrally concerned with change, speed and technology. This article first offers an analysis of White Noise in the light of Virilio’s concept of integral accident in relation to the negative consequences brought about by industrial and technological progress. This is (...) followed by a discussion of the relevance to the novel of Virilio’s theories about architecture and space. Finally, Virilio’s theories about the replacement of conventional war with pure and info wars are discussed in the context of the central event of the novel. Reading the American writer through the lens of the French theorist can shed light on the enduring relevance of both. (shrink)

The larger project broached here is to look at the generally sentence “if X is well-ordered then f is well-ordered”, where f is a standard proof-theoretic function from ordinals to ordinals. It has turned out that a statement of this form is often equivalent to the existence of countable coded ω-models for a particular theory Tf whose consistency can be proved by means of a cut elimination theorem in infinitary logic which crucially involves the function f. To illustrate this theme, (...) we prove in this paper that the statement “if X is well-ordered then εX is well-ordered” is equivalent to . This was first proved by Marcone and Montalban [Alberto Marcone, Antonio Montalbán, The epsilon function for computability theorists, draft, 2007] using recursion-theoretic and combinatorial methods. The proof given here is principally proof-theoretic, the main techniques being Schütte’s method of proof search [Kurt Schütte, Proof Theory, Springer-Verlag, Berlin, Heidelberg, 1977] and cut elimination for a fragment of. (shrink)

We introduce a path-based cyclic proof system for first-order $\mu $-calculus, the extension of first-order logic by second-order quantifiers for least and greatest fixed points of definable monotone functions. We prove soundness of the system and demonstrate it to be as expressive as the known trace-based cyclic systems of Dam and Sprenger. Furthermore, we establish cut-free completeness of our system for the fragment corresponding to the modal $\mu $-calculus.

The article shows a simple way of calibrating the strength of the theory of positive induction, ${{\rm ID}^{*}_{1}}$ . Crucially the proof exploits the equivalence of ${\Sigma^{1}_{1}}$ dependent choice and ω-model reflection for ${\Pi^{1}_{2}}$ formulae over ACA 0. Unbeknown to the authors, D. Probst had already determined the proof-theoretic strength of ${{\rm ID}^{*}_{1}}$ in Probst, J Symb Log, 71, 721–746, 2006.

We present sound and complete sequent calculi for the modal mu-calculus with converse modalities, aka two-way modal mu-calculus. Notably, we introduce a cyclic proof system wherein proofs can be represented as finite trees with back-edges, i.e., finite graphs. The sequent calculi incorporate ordinal annotations and structural rules for managing them. Soundness is proved with relative ease as is the case for the modal mu-calculus with explicit ordinals. The main ingredients in the proof of completeness are isolating a class of non-wellfounded (...) proofs with sequents of bounded size, called slim proofs, and a counter-model construction that shows slimness suffices to capture all validities. Slim proofs are further transformed into cyclic proofs by means of re-assigning ordinal annotations. (shrink)

This article exploits the synergy of critical discourse studies and Corpus Linguistics to study the pervasive representation of Islam and Muslims in an approximate 670,000-word corpus of US news media stories published between 2001 and 2015. Following collocation and concordance analysis of the most frequent topics or categories which revolve around the representation of Islam and Muslims in US news stories, the Discourse-Historical Approach to critical discourse analysis was adopted to investigate how the discursive strategies of nomination and predication are (...) used in US news media stories. The findings indicated that, in general, Islam and Muslims are associated with violence, religious radicalism, and Islamic extremist militants. Finally, the article discusses the discursive themes resulting from the analysis of personal pronouns as well as the educational implications of the findings for social studies and multicultural education. (shrink)

Our world suffers. Some people suffer more than others. Since the first part of 2020, ours is justly described as a time of uncertainty, threat, and upheaval. In this article, we offer reflections threaded narratively, told from the specificity of our societal contexts in Iran, Canada, and Australia. What might we learn in the present and anticipated future from people living chronically within conditions of uncertainty and immobility and also those experiencing uncertainty and immobility for the first time? We argue (...) that reflexive comparative analysis bridging social and visual analysis, anchored in embodied conditions of such people, offers a way to learn from responses to COVID-19 while also being an exercise in ethical research practice. This reflection builds on and extends from our scholarly collaborations that have been ongoing since 2015. Our title recognizes this specific virus as stealthy. Importantly, our choice of words identifies resident Iranians—whose experiences were the original impetuses for this paper, and whose lives provide its empirical basis —as equally steely. (shrink)

To date, of essential goals in psychiatry and establishment of future medical centers is creating therapeutic environments with the aim of improving clinical outcomes, preventing the progression of personality difficulties to serious psychiatric disorders, increasing self-satisfaction in society, facilitating personal growth and actualization, as well as reducing high medical costs. In this regard, the Personality Modulation Clinic in 2016 in Tabriz University of Medical Sciences was established, with the aim of providing appropriate mental health services for clients who do not (...) fulfill criteria for a specific mental disorder, in the traditional classifications; nevertheless, desiring to eliminate inner obstacles towards mental growth, self-actualization, spirituality and the proper well-being they lack. The services in this clinic provide clients with support in order to seek innovative growth opportunities within themselves, by removing inner obstacles towards personality development. These obstacles are roughly equivalent to the diagnosis of “personality difficulty” in the 11th edition of the International Classification of Diseases (ICD-11). Moreover, the therapeutic foundation of this clinic is an emerging medical paradigm known as Cosmetic Psychiatry. At the beginning of any new scientific establishment, as usually happens, and was true for this clinic as well, the bond of philosophical concepts are unveiled, and this is the irreversible and undeniable link between science and philosophy. Thereby, important questions appeared, which were approached philosophically. (shrink)