Kind Of Semantics Research Articles

A logic for reasoning about the probability of fuzzy events

In this paper we present the logic FP ( Ł n , Ł ) which allows to reason about the probability of fuzzy events formalized by means of the notion of state in a MV-algebra. This logic is defined starting from a basic idea exposed by Hájek [Metamathematics of Fuzzy Logic, Kluwer, Dordrecht, 1998]. Two kinds of semantics have been introduced, namely the class of weak and strong probabilistic models. The main result of this paper is a completeness theorem for the logic FP ( Ł n , Ł ) w.r.t. both weak and strong models. We also present two extensions of FP ( Ł n , Ł ) : the first one is the logic FP ( Ł n , RPL ) , obtained by expanding the FP ( Ł n , Ł ) -language with truth-constants for the rationals in [ 0 , 1 ] , while the second extension is the logic FCP ( Ł n , Ł Π 1 2 ) allowing to reason about conditional states.

Stochastic and Real Time in Process Algebra: A Conceptual Overview

It is widely recognized that dealing with time related aspects in process algebra is often crucial for the specification and analysis of complex real systems. Research work in this field has led to a rather huge literature, where several kinds of time have been taken into account: time may be either based on a discrete or continuous domain, time elapsing may be either probabilistically (so-called stochastic-time) or deterministically (so-called real-time) bounded. In this paper we perform a conceptual dissertation about the treatment of the various kinds of time in transition systems where notions of composition are defined (as e.g. by defining a process algebra). We discuss general problems which are independent from the kind of time considered (concerning, e.g., the usual assumption of maximal progress of actions over time). Moreover, we show the conceptual relationship between the notion of time considered and the kind of semantics (in the sense of classical process algebra literature) which must be adopted for representing such a notion of time in the composition operators.

A presentation of Attentional Semantics

The paper presents the two main assumptions of Attentional Semantics--(A) and (B), and its main aim (C). (A) Conscious experience is determined by attention: there cannot be consciousness without attention. Consciousness is explained as the product of attentional activity. Attentional activity can be performed thanks to a special kind of energy: nervous energy. This energy is supplied by the organ of attention. When we perform attentional activity, we use our nervous energy. This activity directly affects the organ of attention, causing a variation in the state of the nervous energy. This variation constitutes the phenomenal aspect of consciousness. (B) Words are tools to pilot attention. The meanings of words isolate, de-contextualize, "freeze" and classify in an articulated system the ever-changing and multiform stream of our conscious experiences. Each meaning is composed of the sequence of invariable elements that, independently of any individual occurrence of a given conscious experience, are responsible for the production of any instance of that conscious experience. The elements composing the meanings of words are attentional operations: each word conveys the condensed instructions on the attentional operations one has to perform if one wants to consciously experience what is expressed through and by it. (C) Attentional Semantics aims at finding the attentional instruction conveyed by the meanings of words. To achieve this goal, it tries: (1) to identify the sequence of the elementary conscious experiences that invariably accompany, and are prompted by, the use of the word being analyzed; (2) to describe these conscious experiences in terms of the attentional operations that are responsible for their production; and (3) to identify the unconscious and non-conscious operations that, directly or indirectly, serve either as the support that makes it possible for the attentional operations to take place, be completed, and occur in a certain way, or as the necessary complement that makes it possible to execute and implement the activities determined and triggered by the conscious experiences. The origins of Attentional Semantics are also presented, and the methodological problems researchers encounter when analyzing meanings in attentional terms are discussed. Finally, a brief comparison with the other kinds of semantics is made.

Typed Mobile Ambients in Maude

Maude has revealed itself as a powerful tool for implementing different kinds of semantics so that quick prototypes are available for trying examples and proving properties. In this paper we show how to define in Maude two semantics for Cardelli and Gordon's Ambient Calculus. The first one is the operational (reduction) semantics which requires the definition of Maude strategies in order to avoid infinite loops. The second one is a type system defined by Cardelli and Gordon to avoid communication errors. The correctness of that system was not formally proved. We enrich the operational semantics with error rules and prove that well-typed processes do not produce such errors. The type system is highly non-deterministic. We show here one possible way of implementing such non-determinism in the rules.

Meaning as an Inferential Role

While according to the inferentialists, meaning is always a kind of inferential role, proponents of other approaches to semantics often doubt that actual meanings, as they see them, can be generally reduced to inferential roles. In this paper we propose a formal framework for considering the hypothesis of the “general inferentializability of meaning”. We provide very general definitions of both “semantics” and “inference” and study the question which kinds of semantics can be reasonably seen as engendered by inferences. We restrict ourselves to logical constants; and especially to the question of the fesaibility of seeing the meanings of those of classical logic in an inferential way. The answer we reach is positive (although with some provisos).

Truly Empiricist Semantics

In van Fraassen's The Scientific Image we are told that the scientific anti-realist need not appeal to some special (e.g. reductionist) semantics for scientific language. He can allegedly hold – just like his direct opponents typically do – that truth-conditional semantics is appropriate both for claims about the observable and claims about the unobservable. However, I shall point out that this kind of semantics goes badly with the anti-realist's epistemic attitude vis-his the unobservable. In this paper an alternative semantics shall be outlined that is perfectly compatible with the rest of the anti-realist's position. Although this alternative semantics will be seen to fly in the face of the established doctrine in the field, I shall argue that there is currently no good reason not to adopt it. It will further be pointed out that this semantics has something to be recommended from a realist perspective as well.

From Geometry of Interaction to Denotational Semantics

We analyze the categorical foundations of Girard's Geometry of Interaction Program for Linear Logic. The motivation for the work comes from the importance of viewing GoI as a new kind of semantics and thus trying to relate it to extant semantics. In an earlier paper we showed that a special case of Abramsky's GoI situations–ones based on Unique Decomposition Categories (UDC's)–exactly captures Girard's functional analytic models in his first GoI paper, including Girard's original Execution formula in Hilbert spaces, his notions of orthogonality, types, datum, algorithm, etc. Here we associate to a UDC-based GoI Situation a denotational model (a *- autonomous category (without units) with additional exponential structure). We then relate this model to some of the standard GoI models via a fully-faithful embedding into a double-gluing category, thus connecting up GoI with earlier Full Completeness Theorems.

A semantic theory for value-passing processes based on the late approach

A general class of languages for value-passing calculi based on the late semantic approach is defined and a concrete instantiation of the general syntax is given. This is a modification of the standard CCS according to the late approach. Three kinds of semantics are given for this language. First a Plotkin style operational semantics by means of an applicative labelled transition system is introduced. This is a modification of the standard labelled transition system that caters for value-passing according to the late approach. As an abstraction, late bisimulation preorder is given. Then a general class of denotational models for the late semantics is defined. A denotational model for the concrete language is given as an instantiation of the general class. Two equationally based proof systems are defined. The first one, which is value-finitary, i. e. only reasons about a finite number of values at each time, is shown to be sound and complete with respect to this model. The second proof system, a value-infinitary one, is shown to be sound with respect to the model, whereas the completeness is proven later. The operational and the denotational semantics are compared and it is shown that the bisimulation preorder is finer than the preorder induced by the denotational model. We also show that in general the ω -bisimulation preorder is strictly included in the model induced preorder. Finally a value-finitary version of the bisimulation preorder is defined and the full abstractness of the denotational model with respect to it is shown. It is also shown that for CCS L the ω -bisimulation preorder coincides with the preorder induced by the model. From this we can conclude that if we allow for parameterized recursion in our language, we may express processes which coincide in any algebraic domain but are distinguished by the ω -bisimulation. This shows that if we extend CCS L in this way we obtain a strictly more expressive language.

A Semantic Theory for Value-Passing Processes Based on the Late Approach

A general class of languages for value-passing calculi based on the late semantic approach is defined and a concrete instantiation of the general syntax is given. This is a modification of the standard CCS according to the late approach. Three kinds of semantics are given for this language. First a Plotkin style operational semantics by means of an applicative labelled transition system is introduced. This is a modification of the standard labelled transition system that caters for value-passing according to the late approach. As an abstraction, late bisimulation preorder is given. Then a general class of denotational models for the late semantics is defined. A denotational model for the concrete language is given as an instantiation of the general class. Two equationally based proof systems are defined. The first one, which is value-finitary, i. e. only reasons about a finite number of values at each time, is shown to be sound and complete with respect to this model. The second proof system, a value-infinitary one, is shown to be sound with respect to the model, whereas the completeness is proven later. The operational and the denotational semantics are compared and it is shown that the bisimulation preorder is finer than the preorder induced by the denotational model. We also show that in general the omega-bisimulation preorder is strictly included in the model induced preorder. Finally a value-finitary version of the bisimulation preorder is defined and the full abstractness of the denotational model with respect to it is shown. It is also shown that for CCS_L the omega -bisimulation preorder coincides with the preorder induced by the model. From this we can conclude that if we allow for parameterized recursion in our language, we may express processes which coincide in any algebraic domain but are distinguished by the omega-bisimulation. This shows that if we extend CCS_L in this way we obtain a strictly more expressive language.

The Box Algebra=Petri Nets+Process Expressions

The paper describes a Petri net as well as a structural operational semantics for an algebra of process expressions. It specifically addresses this problem for the box algebra, a model of concurrent computation which combines Petri nets and standard process algebras. The main result is that it is possible to obtain a framework where process expressions can be given two, entirely consistent, kinds of semantics: one based on Petri nets, the other on SOS rules. This consistency can also be extended to a partial order semantics.

The Box Algebra=Petri Nets+Process Expressions

The paper describes a Petri net as well as a structural operational semantics for an algebra of process expressions. It specifically addresses this problem for the box algebra, a model of concurrent computation which combines Petri nets and standard process algebras. The main result is that it is possible to obtain a framework where process expressions can be given two, entirely consistent, kinds of semantics: one based on Petri nets, the other on SOS rules. This consistency can also be extended to a partial order semantics.

Milk, Honey, and The Good Life on Moral Twin Earth

Moral naturalism is the view that moral properties, such as lightness and goodness, are in some important sense "natural" properties. Some nat uralists have sought to make good on this idea by deploying a kind of semantics proposed by Hilary Putnam and others. Putnam himself sugges ted this strategy,1 and Richard Boyd has pursued it.2 The kind of semantics proposed by Putnam allows for true synthetic property identity statements, such as that water is H20. If this approach can be applied to moral pre dicates, it therefore opens the door to a kind of "synthetic semantic moral naturalism" according to which, for any moral property, there is a syn thetic truth to the effect that the property is identical to a certain natural property. This strategy has come under attack, however, in an argument by Terence Horgan and Mark Timmons known as the "Moral Twin Earth argument".3 On the one hand, Horgan and Timmons argue, G. E. Moore's "open question argument" defeated the idea that there are any analytically true sentences to the effect that a given moral property is identical to a natural property. On the other hand, they argue, the Moral Twin Earth argument undermines the idea that there are any synthetic truths to the effect that a given moral property is identical to a natural property. If they are correct, naturalism is in trouble.4 Are they correct? I will argue that they are not. A close look shows that the Moral Twin Earth argument poses no threat to moral naturalism. To say this is not to say that synthetic moral naturalism is without difficulties. I believe that in fact it has difficulty accounting for the normativity of moral claims. My goal in this paper, however, is the modest one of making Moral Twin Earth safe for naturalists.

The Adaptive Logic of Compatibility

This paper describes the adaptive logic of compatibility and its dynamic proof theory. The results derive from insights in inconsistency-adaptive logic, but are themselves very simple and philosophically unobjectionable. In the absence of a positive test, dynamic proof theories lead, in the long run, to correct results and, in the short run, sometimes to final decisions but always to sensible estimates. The paper contains a new and natural kind of semantics for S5from which it follows that a specific subset of the standard worlds-models is characteristic for S5.

On denotational completeness

The founding idea of linear logic is the duality between A and A ⊥, with values in ⊥. This idea is at work in the original denotational semantics of linear logic, coherent spaces, but also in the phase semantics of linear logic, where the “bilinear form” which induces the duality is nothing but the product in a monoid M , ⊥ being an arbitrary subset B of M . The rather crude phase semantics has the advantage of being complete, and against all predictions, this kind of semantics had some applications. Coherent semantics is not complete for an obvious reason, namely that the coherent space K interpreting ⊥ is too small (one point), hence the duality between A and A ⊥ expressed by the cut-rule cannot be informative enough. But K is indeed the simplest case of a Par-monoid, i.e. the dual of a comonoid, and it is tempting to replace K with any commutative Par-monoid P . Now we can replace coherent spaces with “free P -modules over P ”, linear maps with “ P -linear maps”, with the essential result that all usual constructions remain unchanged: technically speaking cliques are replaced with P -cliques and that is it. The essential intuition behind P is that it accounts for arbitrary contexts: instead of dealing with Γ, A, one deals with A, but a clique of Γ, A can be seen as a P -clique in A. In particular, all logical rules are now defined only on the main formulas of rules, as operations on P -cliques. The duality between A and A ⊥ yields a P -clique in K , i.e. a clique in P ; strangely enough, one must keep the phase layer, i.e. a monoid M (useful in the degenerated case), and the result of the duality is a MP -clique. We specify an arbitrary set B of such cliques as the interpretation of ⊥. Soundness and completeness are then easily established for closed Π 1-formulas, i.e. second-order propositional formulas without existential quantifiers. We must however find the equivalent of 1 ∈ F (which is the condition for being a “provable fact”): a MP -clique is essential when it does not make use of M and P , i.e. when it is induced by a clique in A •. We can now state the theorem: Let A be a closed Π 1 formula, and let a be a clique in the (usual) coherent interpretation A • of A, which is the interpretation of a proof of A; then a ( as an essential clique), belongs to the “denotational fact” A° interpreting A for all M, P and B . Conversely any essential clique with this property comes from a proof of A.

On model, memory management and interface in EDBMS/3

Engineering application domains need database management systems to supply them with a good means of modeling, a high data access efficiency and a language interface with strong functionality. This paper presents a semantic hypergraph model based on relations, in order to express many—to—many relations among objects belonging to different semantic classes in engineering applications. A management mechanism expressed by the model and the basic data of engineering databases are managed in main memory. Especially, different objects are linked by different kinds of semantics defined by users, therefore the table swap, the record swap and some unnecessary examinations are reduced and the access efficiency of the engineering data is increased. C language interface that includes some generic and special functionality is proposed for closer connection with application programs.

Comments on Peter Roeper's “The Link Between Probability Functions and Logical Consequence”

Professor Roeper adresses a large question, whether probabilistic semantics is a kind of semantics at all. Happily, he does this via an exploration of a specific issue on which he and Professor Leblanc have done important work. That is the issue of how the relationship of logical consequence can be characterized as a relation denned in terms of probability. Let us follow him in calling a relevant relationship of the latter sort the degree of implication, and follow Professor Roeper on his quest for a satisfactory one.

On denotational completeness extended abstract

The founding idea of linear logic is the duality between A and A⊥, with values in ⊥. This idea is at work in the original denotational semantics of linear logic, coherent spaces, but also in the phase semantics of linear logic, where the ⪡ bilinear form ⪢ which induces the duality is nothing but the product in a monoid 𝕄, ⊥ being an arbitrary subset 𝔹 of 𝕄. The rather crude phase semantics has the advantage of being complete, and against all predictions, this kind of semantics had some applications. Coherent semantics is not complete for an obvious reason, namely that the coherent space 𝕜 interpreting ⊥ is too small (one point), hence the duality between A and A⊥ expressed by the cut-rule cannot be informative enough. But 𝕜 is indeed the simplest case of a Par-monoid, i.e. the dual of a comonoid, and it is tempting to replace 𝕜 with any commutative Par-monoid ℙ. Now we can replace coherent spaces with ⪡ free P-modules over ℙ ⪢, linear maps with « ℙ-linear maps», with the essential result that all usual constructions remain unchanged: technically speaking cliques are replaced with ℙ-cliques and that's it. The essential intuition behind ℙ is that it accounts for arbitrary contexts: instead of dealing with Г, A, one deals with A, but a clique of Г, A can be seen as a ℙ-clique in A. In particular all logical rules are now defined only on the main formulas of rules, as operations on ℙ-cliques. The duality between A and A⊥ yields a ℙ-clique in ▪, i.e. a clique in ℙ; strangely enough, one must keep the phase layer, i.e. a monoid 𝕄 (useful in the degenerated case), and the result of the duality is a 𝕄ℙ-clique. We specify an arbitrary set 𝔹 of such cliques as the interpretation of ⊥. Soundness and completeness are then easily established for closed π1-formulas, i.e. second-order propositional formulas without existential quantifiers. We must however find the equivalent of 1 ∈ F (which is the condition for being a ⪡ provable fact ⪢): a Mℙ-clique is essential when it does not make use of 𝕄 and ℙ, i.e. when it is induced by a clique in A∗. We can now state the theorem:Let A be a closed π1formula, and let a be a clique in the (usual) coherent interpretation A∗ of A, which is the interpretation of a proof of A; then a (as an essential clique), belongs to the ⪡ denotational fact ⪢ A° interpreting A for all 𝕄, ℙ and 𝔹. Conversely any essential clique with this property comes from a proof of A.

Formal query languages for secure relational databases

The addition of stringent security specifications to the list of requirements for an application poses many new problems in DBMS design and implementation, as well as database design, use, and maintenance. Tight security requirements, such as those that result in silent masking of witholding of true information from a user or the introduction of false information into query answers, also raise fundamental questions about the meaning of the database and the semantics of accompanying query languages. In this paper, we propose a belief-based semantics for secure databases, which provides a semantics for databases that can “lie” about the state of the world, or about their knowledge about the state of the world, in order to preserve security. This kind of semantics can be used as a helpful retrofit for the proposals for a “multilevel secure” database model (a particularly stringent form of security), and may be useful for less restrictive security policies as well. We also propose a family of query languages for multilevel secure relational database applications, and base the semantics of those languages on our semantics for secure databases. Our query languages are free of the semantic problems associated with use of ordinary SQL in a multilevel secure context, and should be easy for users to understand and employ.

The changing role ofentia rationis in mediaeval semantics and ontology: A comparative study with a reconstruction

In this paper I want to argue for two theses concerning entia rationis. My first thesis is that entia rationis, in what I would call the via antiqua1 sense, are objects of thought and signification, required by a certain kind of semantics, but undesirable as objects simpliciter in ontology. My second thesis is that this systematic role of entia rationis in the via antiqua tradition of mediaeval thought was simply eliminated by the advent of Ockhamist semantics, which opened the way towards a radical reinterpretation of the concept of entia rationis and towards a new research programme for ontology. In the next section of this paper, therefore, I start my discussion with a case study of the systematic role played by entia rationis in the philosophy of St. Thomas Aquinas, a typical representative of the via antiqua tradition, occasionally drawing parallels with and taking illustrations from the works of other mediaeval thinkers, too.2 In the third section I give a systematic account of all kinds of entia rationis against the background of a comprehensive semantic theory constructed in the spirit of the via antiqua tradition. In the fourth section I describe the ways William Ockham's approach changed this semantic back ground, and examine how these changes influenced the concept of entia rationis. In the concluding section of the paper I present a simple formal reconstruction of what I take to be Ockham's basic innovations in semantics, and discuss briefly the new ontological programme it in itiated.

The formal language of recursion

This is the first of a sequence of papers in which we will develop a foundation for the theory of computation based on a precise, mathematical notion of abstract algorithm. To understand the aim of this program, one should keep in mind clearly the distinction between an algorithm and the object (typically a function) computed by that algorithm. The theory of computable functions (on the integers and on abstract structures) is obviously relevant to this work, but we will focus on making rigorous and identifying the mathematical properties of the finer (intensional) notion of algorithm.It is characteristic of this approach that we take recursion to be a fundamental (primitive) process for constructing algorithms, not a derived notion which must be reduced to others—e.g. iteration or application and abstraction, as in the classical λ-calculus. We will model algorithms by recursors, the set-theoretic objects one would naturally choose to represent (syntactically described) recursive definitions. Explicit and iterative algorithms are modelled by (appropriately degenerate) recursors.The main technical tool we will use is the formal language of recursion, FLR, a language of terms with two kinds of semantics: on each suitable structure, the denotation of a term t of FLR is a function, while the intension of t is a recursor (i.e. an algorithm) which computes the denotation of t. FLR is meant to be intensionally complete, in the sense that every (intuitively understood) “algorithm” should “be” (faithfully modelled, in all its essential properties by) the intension of some term of FLR on a suitably chosen structure.