Propositional System Research Articles

In the full propositional logic, [formula omitted] of classical tautologies are intuitionistically valid

We present a quantitative comparison of classical and intuitionistic logics, based on the notion of density, within the framework of several propositional languages. In the most general case–the language of the “full propositional system”–we prove that the fraction of intuitionistic tautologies among classical tautologies of size n tends to 5/8 when n goes to infinity. We apply two approaches, one with a bounded number of variables, and another, in which formulae are considered “up to the names of variables”. In both cases, we obtain the same results. Our results for both approaches are derived in a unified way based on structural properties of formulae. As a by-product of these considerations, we present a characterization of the structures of almost all random tautologies.

What Basic Emotions Are Experienced in Bipolar Disorder?

The aims of this study were to investigate the basic emotions experienced within and between episodes of bipolar disorder and, more specifically, to test the predictions made by the Schematic, Propositional, Analogical and Associative Representation Systems (SPAARS) model that mania is predominantly characterized by the coupling of happiness with anger whereas depression (unipolar and bipolar) primarily comprises a coupling between sadness and disgust. A cross-sectional design was employed to examine the differences within and between the bipolar, unipolar and control groups in the emotional profiles. Data were analysed using one-way ANOVAs. Psychiatric diagnoses in the clinical groups were confirmed using the Structured Clinical Interview for DSM-IV (SCID). It was not administered in the control group. Current mood state was measured using the Beck Depression Inventory-II, the State-Trait Anxiety Inventory and the Bech-Rafaelsen Mania Scale. The Basic Emotions Scale was used to explore the emotional profiles. The results confirmed the predictions made by the SPAARS model about emotions in mania and depression. Outwith these episodes, individuals with bipolar disorder experienced elevated levels of disgust. Evidence was found in support of the proposal of SPAARS that there are five basic emotions, which form the basis for both normal emotional experience and emotional disorders. Disgust is an important feature of bipolar disorder. Strengths and limitations are discussed, and suggestions for future research are explored.

A Logic for Vagueness

This paper presents F, substructural logic designed to treat vagueness. Weaker than Lukasiewicz’s infinitely valued logic, it is presented first in a natural deduction system, then given a Kripke semantics in the manner of Routley and Meyer's ternary relational semantics for R and related systems, but in this case, the points are motivated as degrees to which the truth could be stretched. Soundness and completeness are proved, not only for the propositional system, but also for its extension with first-order quantifiers. The first-order models allow not only objects with vague properties, but also objects whose very existence is a matter of degree.

Lattice-valued modal propositional logic and its completeness

Based on the concept of the complete lattice satisfying the first and second infinite distributive laws, the present paper introduces the semantics of the lattice-valued modal propositional logic. It is pointed out that this semantics generalizes the semantics of both classical modal propositional logic and [0, 1]-valued modal propositional logic. The definition of the QMR 0-algebra is proposed, and both the Boole-typed latticevalued modal propositional logic system B and the QMR 0-typed lattice-valued modal propositional logic system QML* are constructed by use of Boole-algebras and QMR 0-algebras, respectively. The main results of the paper are the completeness theorems of both the system B and QML*.

Some properties of fuzzy reasoning in propositional fuzzy logic systems

In order to analyze the logical foundation of fuzzy reasoning, this paper first introduces the concept of generalized roots of theories in Łukasiewicz propositional fuzzy logic Łuk, Gödel propositional fuzzy logic Göd, Product propositional fuzzy logic Π, and nilpotent minimum logic NM (the R 0-propositional fuzzy logic L ∗ ). Next, it is proved that all consequences of a theory Γ, named D( Γ), are completely determined by its generalized root whenever Γ has a generalized root. Moreover, it is proved that every finite theory Γ has a generalized root, which can be expressed by a specific formula. Finally, we demonstrate the existence of a non-fuzzy version of Fuzzy Modus Ponens (FMP) in Łuk, Göd, Π and NM ( L ∗ ) , and we provide its numerical version as a new algorithm for solving FMP.

A new algebraic model for implementing expert systems represented under the ‘Concept-Attribute-Value’ paradigm

This paper is concerned with expounding a new representation paradigm for modeling expert systems based on computing Groebner Bases. Previous research on Groebner Bases expert systems has so far been connected to modeling expert systems based on propositional logics. Our approach instead is based on the well-known Artificial Intelligence ‘Concept-Attribute-Value’ paradigm for representing knowledge. More precisely, our research is based on translating an already existent expert system described in terms of the ‘Concept-Attribute-Value’ paradigm to a new algebraic model which represents knowledge by means of polynomials. In this way, issues about consistence and inference within this expert system will be, through this new model, transformed into algebraic problems involving calculating Groebner Bases. By using this new model of ours, some interesting advantages ensue: on the one hand, knowledge representation may be performed in a more straightforward and intuitive way; on the other, calculating the Groebner Bases associated to our algebraic model is usually faster adopting this new ‘Concept-Attribute-Value’-based paradigm than it was in previous propositional logic-based expert systems.

LIGAÇÕES INTERMEDIÁRIAS E REPRESENTAÇÃO PERSPÍCUA EM WITTGENSTEIN

A noção de ligações intermediárias de sentido, que se revelam através de comparações entre jogos de linguagem, indica os objetos excelsos de incidência de uma investigação conceitual – cujo contexto de elementos pertinentes é progressivamente ampliado por Wittgenstein. Na sua operação negativa, tal noção é profilática contra a atitude filosófica de se buscar um solo último e definitivo para o problema da forma de apresentação. Na sua operação positiva, é a ferramenta conceitual que permitirá o passo crucial de se relativizar os sistemas proposicionais fechados. Mas talvez o pleno alcance do uso de 'ligações intermediárias' se revele ao nos perguntarmos se diversidade de cenas panorâmicas da forma perspícua de representação de conceitos -cerne do “novo método” filosófico proposto por Wittgenstein- não apenas inclui casos intermediários, de forma acessória, mas, mais do que isso, é constituída por esses.

Questions and responses in Yélî Dnye, the Papuan language of Rossel Island

A corpus of 350 naturally-occurring questions in videotaped interaction shows that questions and their responses in Yélî Dnye (the Papuan language of Rossel Island) both conform to clear universal expectations but also have a number of language-specific peculiarities. They conform in that polar and wh-questions are unrelated in form, wh-questions have the usual sort of special forms, and responses show the same priorities as in other languages (for fast cooperative, adequate answers). But, less expected perhaps, Yélî Dnye polar questions (excepting tags) are unmarked in both morphosyntax and prosody, and the responses include conventional facial expressions, conforming to the propositional response system type (so that assent to ‘He didn’t come?’ means ‘no, he didn’t’). These visual signals are facilitated by high levels of mutual gaze making rapid early responses possible. Tags can occur with non-interrogative illocutionary forces, and could be held to perform speech acts of their own. Wh-questions utilize about a dozen wh-forms, which are only optionally fronted, and there are some interesting specializations of forms (e.g. ‘who’ for any named entities other than places). Most questions of all types are genuinely information seeking, with 27% (mostly tags) seeking confirmation, 19% requesting repair.

A systematics of deontic action logics based on Boolean algebra

Within the scope of interest of deontic logic, systems in which names of actions are arguments of deontic operators (deontic action logic) have attracted less interest than purely propositional systems. However, in our opinion, they are even more interesting from both theoretical and practical point of view. The fundament for contemporary research was established by K. Segerberg, who introduced his systems of basic deontic logic of urn model actions in early 1980s. Nowadays such logics are considered mainly within propositional dynamic logic (PDL). Two approaches can be distinguished: in one of them deontic operators are introduced using dynamic operators and the notion of violation, in the other at least some of them are taken as primitive. The second approach may be further divided into the systems based on Boolean algebra of actions and the systems built on the top of standard PDL.In the present paper we are interested in the systems of deontic action logic based on Boolean algebra. We present axiomatizations of six systems and set theoretical models for them. We also show the relations among them and the position of some existing theories on the resulting picture. Such a presentation allows the reader to see the spectrum of possibilities of formalization of the subject.

The generalized truth degree of quantitative logic in the logic system Ln∗ (n-valued NM-logic system)

The concept of the truth degree of a formula is the crucial tool and the building block in quantitative logic, from which the concept of logic metric in quantitative logic is derived. Logic metric takes an important role in quantitative logic, related to which are other concepts in quantitative logic such as divergence, consistency, etc. In the present paper, having combined the theory of generalized tautologies with the theory of truth degrees in quantitative logic, we have proposed the theory of Σ Γ -truth degrees of formulas related to theory Γ in the logic system L n ∗ ( n -valued N M -logic system), and discussed some of its properties. With the help of the properties of Σ Γ -truth degrees: τ Γ ( A ) + τ Γ ( A → B ) ≤ 1 + τ Γ ( B ) , we have obtained the Γ -logic metric on the set F ( S ) of formulas in the propositional logic system L n ∗ ( n -valued N M -logic system). By the work of this paper we can generalize the theory of quantitative logic in all-round way and establish an approximate reasoning’s framework related to theory Γ in the logic system L n ∗ ( n -valued N M -logic system).

Linguistic truth-valued lattice-valued propositional logic system ℓ P( X) based on linguistic truth-valued lattice implication algebra

In the semantics of natural language, quantification may have received more attention than any other subject, and syllogistic reasoning is one of the main topics in many-valued logic studies on inference. Particularly, lattice-valued logic, a kind of important non-classical logic, can be applied to describe and treat incomparability by the incomparable elements in its truth-valued set. In this paper, we first focus on some properties of linguistic truth-valued lattice implication algebra. Secondly, we introduce some concepts of linguistic truth-valued lattice-valued propositional logic system ℓ P( X), whose truth-valued domain is a linguistic truth-valued lattice implication algebra. Then we investigate the semantic problem of ℓ P( X). Finally, we further probe into the syntax of linguistic truth-valued lattice-valued propositional logic system ℓ P( X), and prove the soundness theorem, deduction theorem and consistency theorem.

Consistency Degrees of Theories in Łukasiewicz Fuzzy andn-Valued Propositional Logic Systems

By means of theory of truth degrees of formulas, according to deduction theorems and completeness theorems, the new concepts of consistency degrees and polar index for general theories in Łukasewicz fuzzy andn-valued propositional logic systems are introduced. Moreover, sufficient and necessary conditions for a theoryΓto be consistent, inconsistent, and fully divergent are obtained. Finally, some important properties of truth degrees of formulas are proposed.

A subclass of Horn CNFs optimally compressible in polynomial time

The problem of Horn Minimization (HM) can be stated as follows: given a Horn CNF representing a Boolean function f, find a shortest possible (optimally compressed) CNF representation of f, i.e., a CNF representation of f which consists of the minimum possible number of clauses. This problem is the formalization of the problem of knowledge compression for speeding up queries to propositional Horn expert systems, and it is known to be NP-hard. There are two subclasses of Horn functions for which HM is known to be solvable in polynomial time: acyclic and quasi-acyclic Horn functions. In this paper we define a new class of Horn functions properly containing both of the known classes and design a polynomial time HM algorithm for this new class.

Eating disorders and multi‐level models of emotion: An integrated model

This paper examines the relationship between emotions, depression and eating disorders. Initially, a review is undertaken of the current state of the research and clinical literature with regard to emotional factors in eating disorders. This literature is then integrated within a version of the multi-level model of emotion proposed by Power and Dalgleish. The aim of this paper is to incorporate a basic emotions, multi-modal perspective into developing a new emotions-based model that offers a theoretical understanding of psychological mechanisms in eating disorders. Within the new Schematic Propositional Analogical Associative Representation System model applied to eating disorders, it is argued that the emotions of anger and disgust are of importance in eating disorders and that the eating disorder itself operates as an inhibitor of emotions within the self. It is hoped that the development of a multi-levelled model of eating disorders will allow for the construction of number of specific testable hypotheses that are relevant to future research into the psychological treatment and understanding of eating disorders.

Eating disorders: A basic emotion perspective

Recent research and theory have started to highlight how eating disorder symptoms are often used to regulate painful emotions. However, there has not been one study that has looked at the contributory effect of all the basic emotions onto disordered eating patterns. This study was designed to address this gap within the literature with a detailed examination of the five basic emotions (anger, sadness, disgust, fear and happiness) in relation to disordered eating patterns. This study used the Basic Emotions Scale and the Hospital Anxiety and Depression Scale to explore levels of emotions within 53 female participants with disordered eating patterns who were recruited from the B-EAT research database. The results showed strong correlations between disordered eating and the four negative emotions, but only anger and sadness were left as significant contributors to disordered eating within the regression analysis. These findings were discussed in relation to the literature, with particular reference being made to the new Schematic Propositional Analogical Associative Representation System for Eating Disorders (SPAARS-ED) model.

Perception of threat from emotions and its role in poor emotional expression within eating pathology

Recent research has documented links between eating disorder (ED) symptomatology and emotional expression deficits. Relevant theoretical models have alluded to the functional role of disordered eating in alleviating affect that is felt to be otherwise unmanageable and threatening. Nevertheless, research examining ED individuals' perceptions of emotional states has been sparse, while empirical studies have predominantly focused on global conceptualizations of emotion, failing to address discrete affect states. The current study had three aims: (a) to determine the relation between ED symptomatology and emotional expression, in a sample of women with ED, in an attempt to confirm previous findings of an inverse relation; (b) to test the hypothesis that women with ED inhibit the expression of emotions perceived as threatening, by examining the relation between emotional expression and perceptions of threat from emotion, while partialling out the effects of depression; and (c) to determine whether, amongst women with ED, perceptions of threat from anger are uniquely associated with emotional inhibition, when the effects of depression and body dissatisfaction are controlled for. Results demonstrated that (a) emotional expression was negatively related with the three Eating Disorders Inventory-3 subscales (drive for thinness, bulimia and body dissatisfaction); (b) perceived threat from emotion, particularly anger, was negatively correlated with emotional expression, when depression was partialled out in the analysis; and (c) perceived threat from anger significantly and uniquely predicted emotional inhibition, over and above the effects of body dissatisfaction and depression, in a sample of women with ED symptomatology. It is suggested that anger may be perceived as particularly threatening amongst women with ED, and play a significant role in the emotional expression difficulties that this population experiences. The implications of the current findings are discussed in line with relevant theory and research, with particular reference to the new Schematic Propositional Analogical Associative Representation System for Eating Disorders (SPAARS-ED) model.

Inexpensive Intelligence Using Procedural Propositional Logic

Implementations of inference engine systems invoke many costs, including the cost of the inference engine itself, the cost of integrating the inference engine, and the cost of specialized personnel needed to create and maintain the system. These costs make a very high return on investment a criterion for incorporating these systems into the corporate portfolio of applications and technologies. Recently, the No Inference Engine Theory (NIET) [8] has been developed for creating procedural propositional logic rule-based systems. The NIET systems are implemented in traditional procedural languages such as C++ and do not need an inference engine or proprietary languages, thus eliminating the cost of the inference engine, the cost of integrating the system, and the cost for knowledge of a proprietary language. In addition, these procedural systems are an order of magnitude faster [8] than inference systems and maintain linear performance. For problems using propositional logic, the procedural systems described in this paper offer dramatically lower costs, higher performance, and ease of integration. Lowering the external costs and eliminating the need for specialized skills should make NIET systems more profitable and lead to the wider use of propositional logic systems in business.

A causal framework for integrating learning and reasoning

AbstractCan the phenomena of associative learning be replaced wholesale by a propositional reasoning system? Mitchell et al. make a strong case against an automatic, unconscious, and encapsulated associative system. However, their propositional account fails to distinguish inferences based on actions from those based on observation. Causal Bayes networks remedy this shortcoming, and also provide an overarching framework for both learning and reasoning. On this account, causal representations are primary, but associative learning processes are not excluded a priori.

Towards an Ontology of Fetishes

Alphonso Lingis (1933– ) is an American continental philosopher and translator who is currently Professor Emeritus of Philosophy at Pennsylvania State University.1 Associated with the phenomenology, existentialism, and the ethical philosophy of Emmanuel Levinas and Maurice Merleau-Ponty, Lingis’s philosophical influences also encompass the literary works of Pierre Klossowski and Yukio Mishima, Michel Tournier, and the postpsychoanalytic theory of Jean-Francois Lyotard, Jacques Lacan, Gilles Deleuze, and Felix Guattari. Lingis’s philosophical concerns are thus similar to those of major continental philosophers such as Immanuel Kant and Friedrich Nietzsche, Edmund Husserl, Martin Heidegger, and Michel Foucault, and with whom he often engages in sustained dialogues on everything from sensuality and anthropology to travelogue, the human body, inanimate objects, the elements, and perception.

QUANTIFIED LOGIC OF AWARENESS AND IMPOSSIBLE POSSIBLE WORLDS

Among the many possible approaches to dealing with logical omniscience, I consider here awareness and impossible worlds structures. The former approach, pioneered by Fagin and Halpern, distinguishes between implicit and explicit knowledge, and avoids logical omniscience with respect to explicit knowledge. The latter, developed by Rantala and by Hintikka, allows for the existence of logically impossible worlds to which the agents are taken to have “epistemological” access; since such worlds need not behave consistently, the agents’ knowledge is fallible relative to logical omniscience. The two approaches are known to be equally expressive in propositional systems interpreted over Kripke semantics. In this paper I show that the two approaches are equally expressive in propositional systems interpreted over Montague-Scott (neighborhood) semantics. Furthermore, I provide predicate systems of both awareness and impossible worlds structures interpreted on neighborhood semantics and prove the two systems to be equally expressive.