Conservative Extension Research Articles

Modulated logics and flexible reasoning

This paper studies a family of monotonic extensions of first-order logic which we call modulated logics, constructed by extending classical logic through generalized quantifiers called modulated quantifiers. This approach offers a new regard to what we call flexible reasoning. A uniform treatment of modulated logics is given here, obtaining some general results in model theory. Besides reviewing the “Logic of Ultrafilters”, which formalizes inductive assertions of the kind “almost all”, two new monotonic logical systems are proposed here, the “Logic of Many” and the “Logic of Plausibility”, that characterize assertions of the kind “many”, and “for a good number of”. Although the notion of simple majority (“more than half”) can be captured by means of a modulated quantifier semantically interpreted by cardinal measure on evidence sets, it is proven that this system, although sound, cannot be complete if checked against the intended model. This justifies the interest on a purely qualitative approach to this kind of quantification, what is guaranteed by interpreting the modulated quantifiers as notions of families of principal filters and reduced topologies, respectively. We prove that both systems are conservative extensions of classical logic that preserve important properties, such as soundness and completeness. Some additional perspectives connecting our approach to flexible reasoning through modulated logics to epistemology and social choice theory are also discussed.

HMF

HMF is a conservative extension of Hindley-Milner type inference with first-class polymorphism. In contrast to other proposals, HML uses regular System F types and has a simple type inference algorithm that is just a small extension of the usual Damas-Milner algorithm W. Given the relative simplicity and expressive power, we feel that HMF can be an attractive type system in practice. There is a reference implementation of the type system available online together with a technical report containing proofs (Leijen 2007a,b).

Non-conservative surface decoration of hemoglobin: Influence of neutralization of positive charges at PEGylation sites on molecular and functional properties of PEGylated hemoglobin

High hydrodynamic volume, high viscosity and high colloidal osmotic pressure (COP) of PEGylated hemoglobin (Hb) have been suggested to neutralize the vasoactivity of acellular Hb. Consequences of non-conservative PEGylation (positive charge of the amino groups at the PEGylation sites is neutralized) using succinimidyl-ester of propionic acid PEG5K on the properties of PEGylated Hb have now been investigated. Non-conservative PEGylation of Hb leads to a much higher increase in the COP and viscosity of Hb than conservative extension arm facilitated (EAF) PEGylation of Hb. Introduction of αα-fumaryl crosslinking decreased the COP of non-conservative PEGylated Hb by stabilization of interdimeric interactions. Compared to the EAF-PEGylated αα-fumaryl Hb, non-conservative PEGylated product shows a comparable COP and higher viscosity. Conservative PEGylation of αα-fumaryl Hb by reductive alkylation chemistry does not increase the COP to this level, but enhanced the molecular volume and viscosity comparable to EAF-PEGylated product. Thus, the molecular properties of PEGylated Hb can be fine tuned using different PEGylation platforms and provide a unique opportunity for the design of second generation PEGylated Hbs.

Maude Object-Oriented Action Tool

Object-Oriented Action Semantics (OOAS) incorporates object-oriented concepts to the Action Semantics formalism. Its main goal is to obtain more readable and reusable semantics specifications. Moreover, it supports syntax-independent specifications, due to the way classes are written. Maude Object-Oriented Action Tool (MOOAT) is an executable environment for Object-Oriented Action Semantics implemented as a conservative extension of Full Maude and Maude MSOS Tool (MMT). The Modular SOS of Action Notation has been implemented using MMT transitions and Full Maude has been used to implement the Classes Notation. The syntax created by MOOAT is fairly similar to the original Object-Oriented Action Semantics syntax. In addition to it, the tool combines the modularity aspects observed in the object-oriented approach with the efficient execution and analysis of the Maude system. We use MOOAT to describe syntax-independent specifications of programming languages. In this way, we show how Constructive Object-Oriented Action Semantics (COOAS) may be achieved as a combination between Object-Oriented Action Semantics and Constructive Action Semantics (CAS) using MOOAT, in order to increase the modularity aspects observed in the object-oriented formalism. This paper reports on the development of Maude Object-Oriented Action Tool and its application to the formal specification of programming languages.

FeatherTrait

In the context of statically typed, class-based languages , we investigate classes that can be extended with trait composition. A trait is a collection of methods without state; it can be viewed as an incomplete stateless class . Traits can be composed in any order, but only make sense when imported by a class that provides state variables and additional methods to disambiguate conflicting names arising between the imported traits. We introduce FeatherTrait Java (FTJ), a conservative extension of the simple lightweight class-based calculus Featherweight Java (FJ) with statically typed traits . In FTJ, classes can be built using traits as basic behavioral bricks; method conflicts between imported traits must be resolved explicitly by the user either by (i) aliasing or excluding method names in traits, or by (ii) overriding explicitly the conflicting methods in the class or in the trait itself. We present an operational semantics with a lookup algorithm, and a sound type system that guarantees that evaluating a well-typed expression never yields a message-not-understood run-time error nor gets the interpreter stuck. We give examples of the increased expressive power of the trait-based inheritance model. The resulting calculus appears to be a good starting point for a rigorous mathematical analysis of typed class-based languages featuring trait-based inheritance.

Modular Reuse of Ontologies: Theory and Practice

In this paper, we propose a set of tasks that are relevant for the modular reuse of ontologies. In order to formalize these tasks as reasoning problems, we introduce the notions of conservative extension, safety and module for a very general class of logic-based ontology languages. We investigate the general properties of and relationships between these notions and study the relationships between the relevant reasoning problems we have previously identified. To study the computability of these problems, we consider, in particular, Description Logics (DLs), which provide the formal underpinning of the W3C Web Ontology Language (OWL), and show that all the problems we consider are undecidable or algorithmically unsolvable for the description logic underlying OWL DL. In order to achieve a practical solution, we identify conditions sufficient for an ontology to reuse a set of symbols ``safely''---that is, without changing their meaning. We provide the notion of a safety class, which characterizes any sufficient condition for safety, and identify a family of safety classes--called locality---which enjoys a collection of desirable properties. We use the notion of a safety class to extract modules from ontologies, and we provide various modularization algorithms that are appropriate to the properties of the particular safety class in use. Finally, we show practical benefits of our safety checking and module extraction algorithms.

System BV is NP-complete

System BV is an extension of multiplicative linear logic ( MLL ) with the rules mix, nullary mix, and a self-dual, noncommutative logical operator, called seq. While the rules mix and nullary mix extend the deductive system, the operator seq extends the language of MLL . Due to the operator seq, system BV extends the applications of MLL to those where the sequential composition is crucial, e.g., concurrency theory. System FBV is an extension of MLL with the rules mix and nullary mix. In this paper, by relying on the fact that system BV is a conservative extension of system FBV , I show that system BV is NP-complete by encoding the 3-Partition problem in FBV . I provide a simple completeness proof of this encoding by resorting to a novel proof theoretical method for reducing nondeterminism in proof search, which is also of independent interest.

MAS-ML: a multiagent system modelling language

Multiagent System Modelling Language (MAS-ML) provides a conservative extension to the Unified Modeling Language (UML) 2.1 metamodel in order to accommodate agent-related abstractions such as roles, organisations, plans and protocols. In this paper we present the MAS-ML metamodel by detailing the new concepts introduced in the UML metamodel. In addition, the paper illustrates the new model elements and summarises the three MAS-ML structural diagrams and the two MAS-ML dynamic diagrams.

Role of Extension Arm in PEG-Hb Conjugates on the Stability of the Tetramer: Non-conservative EAF Maleimide Thio-PEG Mediated PEGylation

PEGylation induced increase in colloidal osmotic pressure (COP) of Hb, one of the unique molecular properties of PEG-Hb conjugates, facilitates the neutralization of the vasoconstrictive activity of acellular Hb is a function of chemistry of conjugation of PEG-chains. The dependence of COP with the chemistry is a consequence of PEGylation induced weakening of interdimeric interactions. The conservative Extension Arm Facilitated (EAF) PEGylation exerts least influence on lowering the tetramer stability as compared to direct PEGylation. We have now designed a new, non-conservative EAF PEGylation that uses acylation chemistry to introduce the extension arm onto proteins to delineate the role of the extension arm and of the charge at the site of attachment in PEG-Hb conjugate on tetramer stability. The non-conservative EAF PEGylation does not lower the tetramer stability just as the non-conservative direct PEGylation of Hb. The impact of the extension arm in PEGylated Hb in terms of their structure and potential significance of higher tetramer stability of PEG-Hb conjugates generated by EAF-PEGylation in the in vivo toxicity and in the design of oxygen carrying plasma expander has been discussed.

Arithmetization of the field of reals with exponentiation extended abstract

(1) Shepherdson proved that a discrete unitary commutative semi-ring A + satisfies IE 0 (induction scheme restricted to quantifier free formulas) iff A is integral part of a real closed field; and Berarducci asked about extensions of this criterion when exponentiation is added to the language of rings. Let T range over axiom systems for ordered fields with exponentiation; for three values of T we provide a theory [T] in the language of rings plus exponentiation such that the models (A, exp A ) of [T] are all integral parts A of models M of T with A + closed under exp M and exp A = exp M | A + . Namely T = EXP, the basic theory of real exponential fields; T = EXP+ the Rolle and the intermediate value properties for all 2 x -polynomials; and T = T exp , the complete theory of the field of reals with exponentiation. (2) [T exp ] is recursively axiomatizable iff T exp is decidable. [T exp ] implies LE 0 (x y ) (least element principle for open formulas in the language <, +, x, -1,x y ) but the reciprocal is an open question. [T exp ] satisfies provable polytime witnessing: if (T exp ] proves ∀x∃y: |y| < |x| k )R(x,y) (where |y|:= [log(y)], k < ω and R is an NP relation), then it proves ∀x R(x, f(x)) for some polynomial time function f. (3) We introduce axioms for Arithmetics: axioms which do as if every real number was a fraction (or even a dyadic number). The falsity of such a contention in the standard model of the integers does not mean inconsistency; and bluntness has both a heuristic interest and a simplifying effect on many questions - in particular we prove that the blunt version of [T exp ] is a conservative extension of [T exp ] for sentences in VΔ 0 (x y ) (universal quantifications of bounded formulas in the language of rings plus x y ). Blunt Arithmetics which can be extended to a much richer language could become a useful tool in the non standard approach to discrete geometry, to modelization and to approximate computation with reals.

On Minimal Models

We investigate some logics which use the concept of minimal models in their definition. Minimal objects are widely used in Logic and Computer Science. They are applied in the context of Inductive Definitions, Logic Programming and Artificial Intelligence. An example of logic which uses this concept is the MIN(FO) logic due to van Benthem [20]. He shows that MIN(FO) is equivalent to the Least Fixed Point logic (LFP) in expressive power. In [6], we extended MIN(FO) to the MIN Logic and proved it is equivalent to second-order logic in expressive power. Here, we exhibit a fragment of MIN, the MIN Δ logic, which is more expressive than LFP, less expressive than MIN and closed under boolean connectives and first-order quantification. In order to do this, in the Section 2, we prove that the Downward Lowenheim-Skolem Theorem holds for arbitrary countable sets of LFP-formulas by showing that every infinite structure has a countable LFP-substructure. The method may be used to generalize this theorem to any set of LFP-formulas. We also analyse the expressive power of the Nested Abnormality Theories (NATs) of Lifschitz, another formalism based on minimal models used in Artificial Intelligence, and we demonstrate that for each second-order theory Γ there is a NAT which is a conservative extension of Γ. We give a translation from second-order sentences into such NATs which is linear in the size of the sentence in prenex normal form. Finally, we establish a hierarchy of expressiveness of these logics that deal with the concept of minimal models.

Analytic Calculi for Logics of Ordinal Multiples of Standard t-Norms

For two propositional fuzzy logics, we present analytic proof calculi, based on relational hypersequents. The logic considered first, called MŁ, is based on the finite ordinal sums of Łukasiewicz t-norms. In addition to the usual connectives—the conjunction ⊙, the implication → and the constant 0—we use a further unary connective interpreted by the function associating with each truth value a the greatest ⊙-idempotent below a. MŁ is a conservative extension of Basic Logic. The second logic, called MΠ, is based on the finite ordinal sums of the product t-norm on (0, 1]. Our connectives are in this case just the conjunction and the implication.

A paraconsistent extension of Sylvan’s logic

We deal with Sylvan’s logic CCω. It is proved that this logic is a conservative extension of positive intuitionistic logic. Moreover, a paraconsistent extension of Sylvan’s logic is constructed, which is also a conservative extension of positive intuitionistic logic and has the property of being decidable. The constructed logic, in which negation is defined via a total accessibility relation, is a natural intuitionistic analog of the modal system S5. For this logic, an axiomatization is given and the completeness theorem is proved.

Fair Π

In this paper, we define fair computations in the π-calculus [Milner, R., Parrow, J. & Walker, D., A Calculus of Mobile Processes, Part I and II, Information and Computation 100 (1992) 1–78]. We follow Costa and Stirling's approach for CCS-like languages [Costa, G. & Stirling, C., A Fair Calculus of Communicating Systems, Acta Informatica 21 (1984) 417–441, Costa, G. & Stirling, C., Weak and Strong Fairness in CCS, Information and Computation 73 (1987) 207–244] but exploit a more natural labeling method of process actions to filter out unfair process executions. The new labeling allows us to prove all the significant properties of the original one, such as unicity, persistence and disappearance of labels. It also turns out that the labeled π-calculus is a conservative extension of the standard one. We contrast the existing fair testing [Brinksma, E., Rensink, A. & Vogler, W., Fair Testing, Proc. of CONCUR'95, LNCS, 962 (1995) 313–327, Natarajan, V. & Cleaveland, R., Divergence and Fair Testing, Proc. of ICALP '95, LNCS, 944 (1995) 648–659] with those that naturally arise by imposing weak and strong fairness as defined by Costa and Stirling. This comparison provides the expressiveness of the various fair testing-based semantics and emphasizes the discriminating power of the one already proposed in the literature.

Unwrinkling the Carpet of Meaning

This article is a critical review of Stephen Schiffer’s monograph The Things We Mean. The text discusses some novel contributions made by Schiffer to the philosophy of meaning, in particular, Schiffer’s proposal for the reification of certain abstract entities and the application of his argument to the philosophical problem of vagueness in natural language. Special attention is paid both to Schiffer’s ingenious use of the notion of conservative extension, here employed as a criterion for distinguishing legitimate from illegitimate reifications and to Schiffer’s notion of vague partial belief and its relation to standard partial belief. Schiffer’s particular understanding of vagueness and its relation to the sorites paradox is also considered, with some remarks made concerning the relationship between these related philosophical problems and human perception.

Semantics for a Basic Relevant Logic with Intensional Conjunction and Disjunction

This paper proposes a basic relevant logic B⊓⊔+ with intensional conjunction ⊓ and disjunction ⊔, which are more primitive than those defined by A∘B=df¬(A→¬B) and A+B=df¬A→B. B⊓⊔+ is a conservative extension of the basic relevant logic B+. Stronger logics can be obtained by adding axioms or rules to B⊓⊔+. Kripke style semantics for B⊓⊔+ is given. Three ternary relations R, S1, S2 are used to deal with →, ⊓, and ⊔, respectively. We also consider negation-extensions of B⊓⊔+. The '*' operator is used to model negation.

From Fibring to Cryptofibring. A Solution to the Collapsing Problem

The semantic collapse problem is perhaps the main difficulty associated to the very powerful mechanism for combining logics known as fibring. In this paper we propose cryptofibred semantics as a generalization of fibred semantics, and show that it provides a solution to the collapsing problem. In particular, given that the collapsing problem is a special case of failure of conservativeness, we formulate and prove a sufficient condition for cryptofibring to yield a conservative extension of the logics being combined. For illustration, we revisit the example of combining intuitionistic and classical propositional logics.

Unbound Anaphoric Pronouns: E-Type, Dynamic, and Structured-Propositions Approaches

Unbound anaphoric pronouns or 'E-type pronouns' have presented notorious problems for semantic theory, leading to the development of dynamic semantics, where the primary function of a sentence is not considered that of expressing a proposition that may act as the object of propositional attitudes, but rather that of changing the current information state. The older, 'E-type' account of unbound anaphora leaves the traditional notion of proposition intact and takes the unbound anaphor to be replaced by a full NP whose semantics is assumed to be known (e.g. a definite description). In this paper, I argue that there are serious problems with any version of the E-type account as well as the (original form of the) dynamic account. I will explore a new account based on structured propositions, which can be considered a conservative extension of a traditional proposition-based semantics, but which at the same time incorporates some crucial insights of the dynamic account.

Reference Constructions in the Single-conclusion Proof Logic

We propose an extension of the propositional proof logic language by the second-order variables denoting the reference constructors (like ‘the formula which is proven by x’). The proof logic in this weak second-order language is axiomatized via the calculus ref, the (Functional) Logic of Proofs with References. It is supplied with the formal arithmetical semantics: we prove that ref is sound with respect to arithmetical interpretations and is a conservative extension of propositional single-conclusion proof logic . Finally, we demonstrate how the language of ref can be used as a scheme language for arithmetic and provide the corresponding proof conversion method.

Open Systems Viewed Through Their Conservative Extensions

A typical linear open system is often defined as a component of a larger conservative one. For instance, a dielectric medium, defined by its frequency dependent electric permittivity and magnetic permeability is a part of a conservative system which includes the matter with all its atomic complexity. A finite slab of a lattice array of coupled oscillators modelling a solid is another example. Assuming that such an open system is all one wants to observe, we ask how big a part of the original conservative system (possibly very complex) is relevant to the observations, or, in other words, how big a part of it is coupled to the open system? We study here the structure of the system coupling and its coupled and decoupled components, showing, in particular, that it is only the systemrsquo;s unique minimal extension that is relevant to its dynamics, and this extension often is tiny part of the original conservative system. We also give a scenario explaining why certain degrees of freedom of a solid do not contribute to its specific heat.