Finding Hard Instances of Satisfiability in Lukasiewicz Logics

We propose the notion of automata over Lukasiewicz many-valued logic, extending fuzzy automata (E. Santos, Info. and Control, vol.13, p.363-377, 1968). Indeed, W-algebras, i.e., algebraic structures related with many-valued Lukasiewicz logic, are made of two semiring reducts obtained considering the supremum operation together with the Lukasiewicz conjunction and the infimum operation together with Lukasiewicz disjunction. Vice-versa, given two semirings over the same domain, and given an isomorphism between these two algebras, we can set some conditions in order to have an MV-algebra. Following the tradition of semirings, in this paper, we study "many-valued automata" and "many-valued formal languages" interpreted in Lukasiewicz logic.

This paper proposes a computational framework to reason with conflicting and gradual evidence. The framework is a synthesis of Dung’s seminal work in argumentation semantics with multi-valued logic. Abstract grounded semantics is used to identify the conditions under which a conclusion can be accepted, while multi-valued logic operators are used to quantify the degree of truth of such conditions. We propose a truth-compositional recursive computation based on the notion of irrelevant arguments, and we discuss examples using the major multi-valued logics: Godel’s, Zadeh’s and Łukasiewicz's logic.

Given a finite set of vectors over a finite totally ordered domain, we study the problem of computing a constraint in conjunctive normal form such that the set of solutions for the produced constraint is identical to the original set. We develop an efficient polynomial-time algorithm for the general case, followed by specific polynomial-time algorithms producing Horn, dual Horn, and bijunctive formulas for sets of vectors closed under the operations of conjunction, disjunction, and median, respectively. Our results generalize the work of Dechter and Pearl on relational data, as well as the papers by Hébrard and Zanuttini. They complement the results of Hähnle et al. on multivalued logics and Jeavons et al. on the algebraic approach to constraints.

Resolution-based Theorem Proving for Many-valued Logics

Modern satisfiability (SAT) solvers provide an efficient implementation of classical propositional logic. Their input language, however, is based on the conjunctive normal form (CNF) of propositional formulas. To use SAT solver technology in practice, a user must create the input clauses in one way or another. A typical approach is to write a procedural program that generates formulas on the basis of some input data relevant for the problem domain and translates them into CNF. In this paper, we propose a declarative approach where the intended clauses are specified in terms of rules in analogy to answer set programming (ASP). This allows the user to write first-order specifications for intended clauses in a schematic way by exploiting term variables. We develop a formal framework required to define the semantics of such specifications. Moreover, we provide an implementation harnessing state-of-the-art ASP grounders to accomplish the grounding step of clauses. As a result, we obtain a general-purpose clause-level grounding approach for SAT solvers. Finally, we illustrate the capabilities of our specification methodology in terms of combinatorial and application problems.

The dramatic improvements in Boolean satisfiability (SAT) solving since the turn of the millennium have made it possible to leverage state-of-the-art conflict-driven clause learning (CDCL) solvers for many combinatorial problems in academia and industry, and the use of proof logging has played a crucial role in increasing the confidence that the results these solvers produce are correct. However, the fact that SAT proof logging is performed in conjunctive normal form (CNF) clausal format means that it has not been possible to extend guarantees of correctness to the use of SAT solvers for more expressive combinatorial paradigms, where the first step is an unverified translation of the input to CNF. In this work, we show how cutting-planes-based reasoning can provide proof logging for solvers that translate pseudo-Boolean (a.k.a. 0-1 integer linear) decision problems to CNF and then run CDCL. To support a wide range of encodings, we provide a uniform and easily extensible framework for proof logging of CNF translations. We are hopeful that this is just a first step towards providing a unified proof logging approach that will also extend to maximum satisfiability (MaxSAT) solving and pseudo-Boolean optimization in general.

The aim of the paper is to present an original fuzzy logic based approach for dealing with uncertainties in expert systems. Its essence consists in understanding a knowledge base as a fuzzy axiomatic theory, i.e. a set of formulae in which each formula is assigned a weight specifying the degree of membership in the fuzzy set of special axioms. According to this principle, the task of inference in expert systems can be analyzed from the many-valued (fuzzy) logic perspective. As a result of theoretical considerations, Lukasiewicz's logic is preferred because of its completeness property. The inference mechanism based on this logic has been implemented and compared with the standard in different applications.

Phase transition phenomenon: A compound measure analysis

The studies of time-dependent structural changes in the solvent-induced crystallization and phase transition phenomena have been reviewed by focusing mainly on syndiotactic polystyrene (SPS) and its relatives having the functional groups on the phenyl rings. The time-resolved measurement of X-ray diffraction and vibrational spectra has revealed the structural evolution process in the solvent-induced crystallization of SPS, which depends on the type (polarity, bulkiness, etc.) of the solvent molecules. The heating of the SPS-solvent complexes causes the complicated phase transitions from theδform (complex) to theγform and to theα(orβ) form. The introduction of such a polar functional group as OCH3or halogen units on the phenyl rings enhances the interactions between the SPS and the solvent, the strength of which depends on the substitution position of the OCH3units on the phenyl ring. For example, the ortho- or para-substitution dissolves the sample quite easily at room temperature, while the meta-substitution makes it possible to create the solvent complexes. The discussion has been made for the structural relation before and after the formation of the solvent-complexes.

Optimized solvers for the Boolean satisfiability (SAT) problem have many applications in areas such as hardware and software verification, FPGA routing, planning, and so forth. Further uses are complicated by the need to express "counting constraints" in conjunctive normal form (CNF). Expressing such constraints by pure CNF leads to more complex SAT instances. Alternatively, those constraints can be handled by integer linear programming (ILP), but generic ILP solvers may ignore the Boolean nature of 0-1 variables. Therefore, specialized 0-1 ILP solvers extend SAT solvers to handle these so-called "pseudo-Boolean" (PB) constraints. This work provides an update on the on-going competition between generic ILP techniques and specialized 0-1 ILP techniques. To make a fair comparison, we generalize recent ideas for fast SAT-solving to more general 0-1 ILP problems that may include counting constraints and optimization. This generalization is embodied in our PB constraint solver and optimizer PBS, which is compared with state-of-the-art CNF and generic ILP solvers. Another aspect of our comparison is the evaluation on 0-1 ILP benchmarks that originate in electronic design automation (EDA) but that cannot be directly solved by an SAT solver. Specifically, we solve instances of the max-SAT and max-ONEs optimization problems, which seek to maximize the number of satisfied clauses and the "true" values over all satisfying assignments, respectively. Those problems have straightforward applications to SAT-based routing and are additionally important due to reductions from max-cut, max-clique, and min vertex cover. Our experimental results show that specialized 0-1 techniques implemented in PBS tend to outperform generic ILP techniques on Boolean optimization problems, as well as on general EDA SAT problems.

Boolean satisfiability (SAT) and its extensions are becoming a core technology for the analysis of systems. The SAT-based approach divides into three steps: encoding, preprocessing, and search. It is often argued that by encoding arbitrary Boolean formulas in conjunctive normal form (CNF), structural properties of the original problem are not reflected in the CNF. This should result in the fact that CNF-level preprocessing and SAT solver techniques have an inherent disadvantagecompared to related techniques applicable on the level of more structural SAT instance representations such as Boolean circuits. In this work we study the effect of a CNF-level simplification technique called blocked clause elimination (BCE). We show that BCE is surprisingly effective both in theory and in practice on CNFs resulting from a standard CNF encoding for circuits: without explicit knowledge of the underlying circuit structure, it achieves the same level of simplification as a combination of circuit-level simplifications and previously suggested polarity-based CNF encodings. Experimentally, we show that by applying BCE in preprocessing, further formula reduction and faster solving can be achieved, giving promise for applying BCE to speed up solvers.

Jamming transition of high-dimensional traffic dynamics

Phase transition phenomena take place in aqueous solutions, model foods and cellular tissues subjected to combined high pressure and low (subzero) temperature. The kinetics and mechanisms of pressure-shift nucleation (ice I), of type III, V and VI ice crystal formation, or of pressure-assisted thawing are being thoroughly investigated. Fast data acquisition systems and specific microscopy techniques have revealed that pressure-shift freezing (PSF) induces significant undercooling, and enhances uniform ice nucleation throughout sample depth. Both physical and chemical parameters affect the ice crystal size distribution. These phase transition phenomena, as well as the pressure level, influence chemical constituents (proteins, enzymes) and structural elements (gels, emulsions, cellular tissues, microorganisms). Recent studies indicate that: 1) in PSF of muscle foods (meat, seafoods), the aggregation of myofibrillar proteins and the resulting toughness due to high pressure exposition appear to offset the benefit of small ice crystals; 2) the cell and tissue structure of some fruits or vegetables is less disrupted by PSF than by air-blast freezing, but it is doubtful whether this brings improved appearance, texture or water retention, especially for large samples; 3) high pressure-low temperature inactivation of food enzymes is not sufficient to replace thermal blanching; 4) microbial inactivation under pressure is somewhat enhanced at subzero temperatures in buffer solutions but perhaps less so in food products; 5) the benefits of pressure-assisted thawing in terms of enhanced rate and hygiene (subzero temperature, microbial inactivation) may compensate for increased equipment and packaging costs, especially for seafoods; 6) the formation of type III or V ice in biological samples cooled under pressure requires extensive undercooling; 7) progress is made in modelling pressure-assisted freezing and thawing, and in assessing the extent of pressure-shift nucleation.

First order ferroelectric phase transition phenomenon in alkali-phosphate crystal by using Green’s function approach

In this present work, nanocrystalline powders of Pb-doped LaMnO3 or La0.64Pb0.36MnO3 (LPMO) have been synthesized with various grain sizes by a solid-state reaction method followed by ball milling technique. Based on the dependence of crystallite size, the magnetic properties of the LPMO nanoperovskites have been investigated. The nanoperovskites have been structurally characterized. Further, the synthesized nanoperovskite manganite materials with various grain sizes are systematically studied for ultrasonic longitudinal velocity (UL), shear velocity (US) and longitudinal and shear attenuation (αL and αS) in wide range of temperatures. All the nanoperovskites revealed an anomalous behaviour in concern with ultrasonic velocities and attenuation towards the phenomenon of phase transition.