Showing papers in "Logic Journal of The Igpl \/ Bulletin of The Igpl in 2012"

A logic of agent organizations

Abstract: Organization concepts and models are increasingly being adopted for the design and specification of multi-agent systems. Agent organizations can be seen as mechanisms of social order, created to achieve global (or organizational) objectives by more or less autonomous agents. In order to develop a theory on the relation between organizational structures, organizational objectives and the actions of agents fulfilling roles in the organization a theoretical framework is needed to describe organizational structures and actions of (groups of) agents. Current logical formalisms focus on specific aspects of organizations (e.g. power, delegation, agent actions or normative issues) but a framework that integrates and relates different aspects is missing. Given the amount of aspects involved and the subsequent complexity of a formalism encompassing them all, it is difficult to realize. In this article, a first step is taken to solve this problem. We present a generic formal model that enables us to specify and relate the main concepts of an organization (including, activity, structure, environment and others) so that organizations can be analysed at a high level of abstraction. However, for some aspects we use a simplified model in order to avoid the complexity of combining many different types of (modal) operators.

Projective unification in modal logic

Abstract: A projective unifier for a modal formula A, over a modal logic L, is a unifier σ for A (i.e. a substitution making A a theorem of L) such that the equivalence of σ with the identity map is the consequence of A. Each projective unifier is a most general unifier for A. Let L be a normal modal logic containing S4. We show that every unifiable formula has a projective unifier in L iff L contains S4.3. The syntactic proof is effective. As a corollary, we conclude that all normal modal logics L containing S4.3 are almost structurally complete, i.e. all (structural) admissible rules having unifiable premises are derivable in L. Moreover, L is (hereditarily) structurally complete iff L contains McKinsey axiom M .

Quantum-like non-separability of concept combinations, emergent associates and abduction

Abstract: Consider the concept combination ‘pet human’. In word association experiments, human subjects produce the associate ‘slave’ in relation to this combination. The striking aspect of this associate is that it is not produced as an associate of ‘pet’, or ‘human’ in isolation. In other words, the associate ‘slave’ seems to be emergent. Such emergent associations sometimes have a creative character and cognitive science is largely silent about how we produce them. Departing from a dimensional model of human conceptual space, this article will explore concept combinations, and will argue that emergent associations are a result of abductive reasoning within conceptual space, that is, below the symbolic level of cognition. A tensor-based approach is used to model concept combinations allowing such combinations to be formalized as interacting quantum systems. Free association norm data is used to motivate the underlying basis of the conceptual space. It is shown by analogy how some concept combinations may behave like quantum-entangled (non-separable) particles. Two methods of analysis were presented for empirically validating the presence of non-separable concept combinations in human cognition. One method is based on quantum theory and another based on comparing a joint (true theoretic) probability distribution with another distribution based on a separability assumption using a chi-square goodness-of-fit test. Although these methods were inconclusive in relation to an empirical study of bi-ambiguous concept combinations, avenues for further refinement of these methods are identified.

Social and swarm aspects of co-authorship network

Abstract: The analysis of social networks is concentrated mainly on uncovering hidden relations and properties of network nodes (vertices). Most of the current approaches are focused on different network types and different network coefficients. This article introduces a social network analysis based on the so-called Forgetting Curve and Swarm Intelligence inspired by the Ant Colony Optimization. We analyse a co-authorship network and identify two types of ties among its nodes. The Forgetting Curve and Swarm Intelligence are used to model the dynamics of such a network.

On a pairwise comparison-based consistent non-numerical ranking

Abstract: We discuss a consistent model of pairwise comparison-based non-numerical ranking. An algorithm that enforces consistency for raw or partially organized ranking data is presented and its properties are analysed. The concept of testing subjective rankings is also discussed.

Soundness and completeness of the Cirquent calculus system CL6 for computability logic

Abstract: Computability logic is a formal theory of computability. The earlier article "Introduction to cirquent calculus and abstract resource semantics" by Japaridze proved soundness and completeness for the basic fragment CL5 of computability logic. The present article extends that result to the more expressive cirquent calculus system CL6, which is a conservative extension of both CL5 and classical propositional logic.

Generalized Kripke semantics for the Lambek-Grishin calculus

Abstract: properties. It turns out that this extension is precisely the algebra of Galois closed sets of the canonical frame as defined in section 2 of [Geh06]. Thus we get a simple abstract manner of working with the canonical frame. This makes it easy to treat additional operations and their interaction axioms. In particular, from A = (A,⊗, /, \,⊕,;, ) we get Aδ = (Aδ,⊗σ, / π, \ π,⊕π,; σ, σ) and Aδ is the algebra of Galois closed sets for some frame which we denote by (X,Y,6, R⊗σ , R⊕π) =: F(A). The central role of the canonical extension in the process of finding relational semantics is illustrated by the following diagramme. Lambek-Grishin logic LG-algebras A = (A,⊗, /, \,⊕,;, ) Canonical extensions Aδ ∼= (G(X,Y,6),⊗σ, / π, \ π,⊕π,; σ, σ) Lambek-Grishin frames F(A) = (X,Y,6, R⊗σ , R⊕π) Relational semantics // oo This process works for the Lindenbaum algebra A of the LG∅-logic in the sense that the canonical frame F(A) with the interpretation given by the embedding map is a model of precisely those sequents that are deducible in LG∅, as the following equivalences demonstrate. A ` B holds in LG∅ ⇐⇒ A 6 B holds in A ∗ ⇐⇒ [A]Aδ 6 [B]Aδ holds in A ⇐⇒ F(A) A ` B, where the subscript Aδ means that the formula is interpreted in Aδ. We call A = (A,⊗, /, \,⊕,;, ) an LG-algebra provided A is a poset, and the operations of A satisfy the rules of LG∅, i.e. / and \ are upper residuals of ⊗, while ; and are lower residuals of ⊕. The process of getting a canonical extension and from a canonical extension a Lambek-Grishin frame works for any LG-algebra. When dealing with a class of algebras that satisfy additional interaction axioms (e.g. one of Grishin’s groups, see next section), our aim is to find out which first-order condition is imposed by these axioms on the class of Lambek-Grishin frames. In order to prove the completeness of an axiomatic extension of LG∅, two components are needed: 1. We have to show that if we start with A, the Lindenbaum algebra for some extension of LG∅, then for each additional axiom, the equivalence indicated by ∗ still works. This

A first-order conditional probability logic

Abstract: In this article, we present the probability logic LFOCP which is suitable to formalize statements about conditional probabilities of first order formulas. The logical language contains formulas such as CP s(φ,θ) and CP s(φ,θ) with the intended meaning ‘the conditional probability of φ given θ is at least s’ and ‘at most s’, respectively, where φ and θ are first-order formulas. We introduce a class of first order Kripke-like models that combine properties of the usual Kripke models and finitely additive probabilities. We propose an infinitary axiom system and prove that it is sound and strongly complete with respect to the considered class of models. In this article, the terms finitary and infinitary concern meta language only, i.e. the logical language is countable, formulas are finite, while only proofs are allowed to be infinite. We analyse decidability of LFOCP and provide a procedure which decides satisfiability of a given conditional probability formula, in the case when the underlying first-order theory is decidable. Relationships to other systems and possible extensions of the presented approach are discussed.

Some variants of Vaught’s conjecture from the perspective of algebraic logic

Abstract: Vaught’s Conjecture states that if T is a complete first order theory in a countable language such that T has uncountably many pairwise non-isomorphic countably infinite models, then T has 2^ℵ_0 many pairwise non-isomorphic countably infinite models Continuing investigations initiated in S´agi, we apply methods of algebraic logic to study some variants of Vaught’s conjecture More concretely, let S be a σ-compact monoid of selfmaps of the the natural numbers We prove, among other things, that if a complete first order theory T has at least ℵ1 many countable models that cannot be elementarily embedded into each other by elements of S, then, in fact, T has continuum many such models We also study-related questions in the context of equality free logics and obtain similar results Our proofs are based on the representation theory of cylindric and quasi-polyadic algebras (for details see Henkin, Monk and Tarski (cylindric Algebras Part 1 and Part 2)) and topological properties of the Stone spaces of these algebras

Insolvency prediction for assessing corporate financial health

Abstract: The prediction of corporate financial failure, crucial for the prevention and mitigation of economic downturns in a national economy, requires the categorization of healthy and unhealthy companies. This study examines the case of Serbia and applies multivariant statistical methods and specific artificial neural network architectures—the self-organizing map (SOM)—to assess the corporate financial health of various companies. Financial ratios drawn from corporate balance sheets become the independent variables in a multivariate discriminant analysis (MDA). These financial ratios and the discriminant Z-score in the MDA form the input for the SOM, which creates a hybrid MDA-SOM model that is capable of predicting corporate financial insolvency. The experimental results of this research correctly estimate company financial health in 95% of cases. These are reliable predictions that are comparable with similar studies in other countries.

A Formal Explication Of The Search For Explanations: The Adaptive Logics Approach To Abductive Reasoning

Abstract: Most logic–based approaches characterize abduction as a kind of backwards deduction plus additional conditions, which means that a number of conditions is specified that enable one to decide whether or not a particular abductive inference is sound (one of those conditions may e.g. be that abductive consequences have to be compatible with the background theory). Despite the fact that these approaches succeed in specifying which formulas count as valid consequences of abductive inference steps, they do not explicate the way people actually reason by means of abductive inferences. This is most clearly shown by the absence of a decent proof theory. Instead, search procedures are provided that enable one to determine the right abductive consequences. However, these do not by far resemble human reasoning. In order to explicate abductive reasoning more realistically, an alternative approach will be provided in this article, namely, one that is based on the adaptive logics programme. Proof theoretically, this approach interprets the argumentation schema affirming the consequent (AC:

Hyperidentities of De Morgan algebras

Abstract: The hyperidentities of the variety of De Morgan algebras are characterized in this paper. A finite base of hyperidentities for this variety is found as a consequence. In particular, we obtain that the variety of De Morgan algebras has a decidable hyperequational theory. And finally we prove that the hyperequational theory of this variety is not one-based.

A modal framework for modelling abductive reasoning

Abstract: We present a framework for understanding abduction within modal logic and Kripke semantics; worlds of a Kripke frame will represent possible theories, and a change in theory will be understood as a passage from one world to an adjacent possible world. Further, these steps may agree with the accessibility relation or may ‘backtrack’, accordingly as new information refutes or reinforces our present theory. Our formalism can be used to model not only abduction, but also to talk about the inner structure of theories as well as relations between them, allowing us to interpret many ideas from philosophy of science within the well-understood framework of modal logic.

A Morphological Cellular Automata Based On Morphological Independence

Abstract: We discuss a definition of Morphological Cellular Neural Networks (MCNN) where the state change operator are Auto-associative Morphological Memories (AMM). The fast convergence properties of AMM and the shape of its fixed point set make the MCNN dynamics trivial. However, segmentation results are poor. We propose a Morphological Cellular Automata (MCA) with assured convergence to a state characterized by morphological dependences and independences between neighbouring cell states. Cell dynamic rules test morphological dependence among neighbouring cell’s states. When neighbouring cell states are morphological dependent in the erosive or dilative sense, the morphologically dominant state colonizes the neighbour with morphological dependent state. The resulting configuration of cell states is composed of homogeneous regions whose boundaries are defined by the morphological independence relation. Results are given on image segmentation, where MCA cells correspond to image pixels.

LogAB: A first-order, non-paradoxical, algebraic logic of belief

Abstract: LogAB is a family of logics of belief. It holds a middle ground between the expressive, but prone to paradox, syntactical first-order theories and the often inconvenient, but safe, modal approaches. In this report, the syntax and semantics of LogAB are presented. LogAB is algebraic in the sense that it is a language of only terms; there is no notion of a formula, only proposition-denoting terms. The domain of propositions is taken to be a Boolean algebra, which renders classical truth conditions and definitions of consequence and validity theorems about LogAB structures. LogAB is shown to be sufficiently expressive to accommodate complex patterns of reasoning about belief while remaining paradox-free. A number of results are proved regarding paradoxical self-reference. They are shown to strengthen previous results, and to point to possible new approaches to circumventing paradoxes in syntactical theories of belief.

(Star-Based) three-valued Kripke-style semantics for pseudo- and weak-Boolean logics

Abstract: This article investigates Kripke-style semantics for two sorts of logics: pseudo-Boolean (pB) and weak-Boolean (wB) logics. As examples of the first, we introduce G3 and S5 pB 3 . G3 is the three-valued Dummett–Gödel logic; S5 3 is the modal logic S5 but with its orthonegation replaced by a pB (or Heyting) negation. Examples of wB logic are GwB 3 and S5 wB 3 . G wB 3 is G3 with a wB negation in place of its pB negation; S5 wB 3 is S5 with a wB negation replacing its orthonegation. For each system, we provide a three-valued Kripke-style semantics with and without star operation (which is like the star operation of the Routley–Meyer semantics of relevance logics). We prove soundness and completeness theorems in each case. Note that wB logics may be equivalent to logics with Baaz’s projection . We finally introduce the G3 and the S5 pB 3 both with and show that they are equivalent to G wB 3 and S5wB 3 , respectively.

Relational dual tableau decision procedure for modal logic K

Abstract: We present a dual tableau system, RLK, which is itself a deterministic decision procedure verifying validity of K-formulas. The system is constructed in the framework of the original methodology of relational proof systems, determined only by axioms and inference rules, without any external techniques. Furthermore, we describe an implementation of the system RLK in Prolog, and we show some of its advantages.

Which classical correspondence is valid in intuitionistic modal logic

Abstract: Modal logics reason about properties of relational structures, and such properties are often characterized by axioms of modal logics. This connection between properties of relational structures and axioms of modal logics are called correspondence, and has been investigated well in the classical setting. The problem we consider is an intuitionistic version of this correspondence. In particular, this paper considers which part of the correspondence results known in classical setting is true for intuitionistic one. We first define the notion of robustness of axioms so that an axiom is robust if and only if its corresponding properties in classical and intuitionistic semantics are the same. Next we give a syntactically defined class of axioms, and prove that all axioms in this class are robust. This result is an analogue of the classical result by Sahlqvist, and its proof is partly based on a known proof of his theorem.

Double sequences, almost Cauchyness and BD-N

Abstract: It is shown that, relative to Bishop-style constructive mathematics, the boundedness principle BD-N is equivalent both to a general result about the convergence of double sequences and to a particu ...

Soft computing models to analyze atmospheric pollution issues

Abstract: Multidisciplinary research into statistical and soft computing models is detailed that analyses data on inmissions of atmospheric pollution in urban areas. The research analyzes the impact on atmospheric pollution of an extended bank holiday weekend in Spain. Levels of atmospheric pollution are classified in relation to the days of the week, seeking to differentiate between working days and non-working days by taking account of such aspects as industrial activity and traffic levels. The case of study is based on data collected by a station at the city of Burgos, which forms part of the pollution measurement station network within the Spanish Autonomous Region of Castile-Leon.

Using clustering techniques for intelligent camera-based user interfaces

Abstract: The area of Human-Machine Interface is growing fast due to its high importance in all technological systems. The basic idea behind designing human-machine interfaces is to enrich the communication with the technology in a natural and easy way. Gesture interfaces are a good example of transparent interfaces. Such interfaces must identify properly the action the user wants to perform, so the proper gesture recognition is of the highest importance. However, most of the systems based on gesture recognition use complex methods requiring high-resource devices. In this work, we propose to model gestures capturing their temporal properties, which significantly reduce storage requirements, and use clustering techniques, namely self-organizing maps and unsupervised genetic algorithm, for their classification. We further propose to train a certain number of algorithms with different parameters and combine their decision using majority voting in order to decrease the false positive rate. The main advantage of the approach is its simplicity, which enables the implementation using devices with limited resources, and therefore low cost. The testing results demonstrate its high potential.

Decidability and complexity for ω-regular properties of stochastic systems

Abstract: Herein we study the probabilization of Quantified Linear Temporal Logic, which we call PQLTL. PQLTL can reason about any semialgebraic constrain over probabilities of paths of a Markov chain satisfying a QLTL formulae. PQLTL is related with other commonly used probabilistic temporal logics (such as PLTL, PCTL and PCTL∗) that were devised only to specify properties for which model checking algorithms are amenable and whose basic results, such as completeness and decidability, were never investigated. In this paper, we devise a strong and a weak SAT algorithm for PQLTL. The former relies in [n+2]-EXPSPACE and the latter in [n+1]EXPSPACE where n is the alternation depth of the quantifiers in the input formula. The weak SAT algorithm for the existential fragment, which has all the expressive power of PQLTL, is in EXPSPACE. Another relevant fragment of PQLTL is the linear closure of PCTL∗ without nesting of the probability operator. We show that the SAT problem for this fragment is PSPACE complete. Capitalizing in these results, we derive a complete calculus for PQLTL and illustrate it with a toy example.

An application of a theorem of Rothmaler

Abstract: In this article, the notion of purely large structure is introduced. It is shown, with the aid of a Theorem of Rothmaler, that any finitely accessible class possesses purely large structures. This applies to the class Mod(R) of all left modules over a given ring R. The theory T ∗ of purely large modules is always complete. It is shown that T ∗ is model-complete if and only if R is regular. For any algebra of finite representation type R, over an infinite field, T ∗ is axiomatizable by one sentence over Th(Mod(R)). A characterization of pure semisimple rings, in terms of purely large modules, is obtained.