Compositional verification aims at managing the complexity of theverification process by exploiting compositionality of the systemarchitecture. In this paper we explore the use of a temporal epistemiclogic to formalize the process of verification of compositionalmulti-agent systems. The specification of a system, its properties andtheir proofs are of a compositional nature, and are formalized within acompositional temporal logic: Temporal Multi-Epistemic Logic. It isshown that compositional proofs are valid under certain conditions.Moreover, the possibility of incorporating default persistence ofinformation (...) in a system, is explored. A completion operation on aspecific type of temporal theories, temporal completion, is introducedto be able to use classical proof techniques in verification withrespect to non-classical semantics covering default persistence. (shrink)

Coalition announcement logic is one of the family of the logics of quantified announcements. It allows us to reason about what a coalition of agents can achieve by making announcements in the setting where the anti-coalition may have an announcement of their own to preclude the former from reaching its epistemic goals. In this paper, we describe a PSPACE-complete model checking algorithm for CAL that produces winning strategies for coalitions. The algorithm is implemented in a proof-of-concept model checker.

Our starting point is Michael Luntley's falsificationist semantics for the logical connectives and quantifiers: the details of his account are criticised but we provide an alternative falsificationist semantics that yields intuitionist logic, as Luntley surmises such a semantics ought. Next an account of the logical connectives and quantifiers that combines verificationist and falsificationist perspectives is proposed and evaluated. While the logic is again intuitionist there is, somewhat surprisingly, an unavoidable asymmetry between the verification and falsification conditions for (...) negation, the conditional, and the universal quantifier. Lastly we are lead to a novel characterization of realism. (shrink)

Theorem 1 states a negative result about the classical semantics j= ! of program schemes. Theorem 2 investigates the reason for this. We conclude that Theorem 2 justies the Henkin-type semantics j= for which the opposite of the present Theorem 1 was proved in [1]{[3] and also in a dierent form in part III of [5]. The strongest positive result on j= is Corollary 6 in [3].

Verification and validation of numerical models of natural systems is impossible. This is because natural systems are never closed and because model results are always nonunique. Models can be confirmed by the demonstration of agreement between observation and prediction, but confirmation is inherently partial. Complete confirmation is logically precluded by the fallacy of affirming the consequent and by incomplete access to natural phenomena. Models can only be evaluated in relative terms, and their predictive value is always open to question. (...) The primary value of models is heuristic. (shrink)

In this paper, a timed modal logic L c is presented for the specification and verification of real-time systems. Several important results for L c are discussed. First we address the model checking problem and we show that it is an EXPTIME-complete problem. Secondly we consider expressiveness and we explain how to express strong timed bisimilarity and how to build characteristic formulas for timed automata. We also propose a compositional algorithm for L c model checking. Finally we consider (...) several control problems for which L c can be used to check controllability. (shrink)

The notion of program verification appears to trade upon an equivocation. Algorithms, as logical structures, are appropriate subjects for deductive verification. Programs, as causal models of those structures, are not. The success of program verification as a generally applicable and completely reliable method for guaranteeing program performance is not even a theoretical possibility.

The new phase of science evolution is characterized by totality of subject and object of cognition and technology (high-hume). As a result, forming of network structure in a disciplinary matrix modern are «human dimensional» natural sciences and two paradigmal «nuclei» (attraktors). As a result, the complication of structure of disciplinary matrix and forming a few paradigm nuclei in modern «human dimensional» natural sciences are observed. In the process of social verification integration of scientific theories into the existent system of (...) mental and valued options of spiritual culture takes place. The attribute of classical science – ethics neutrality of scientific knowledge becomes an unattainable ideal. One of the trends in the evolution of theoretical epistemology is the study of migration mechanisms of generation of scientific knowledge from the sphere of its own logic and methodology of science in the field of sociology - the consideration of this process, as the resulting system of interactions of social structures and institutions. Ensuing ideas and settings become the dominant worldview of philosophical and technological civilization. -/- . (shrink)

The new phase of science evolution is characterized by totality of subject and object of cognition and technology (high-hume). As a result, forming of network structure in a disciplinary matrix modern are «human dimensional» natural sciences and two paradigmal «nuclei» (attraktors). As a result, the complication of structure of disciplinary matrix and forming a few paradigm nuclei in modern «human dimensional» natural sciences are observed. In the process of social verification integration of scientific theories into the existent system of (...) mental and valued options of spiritual culture takes place. The attribute of classical science – ethics neutrality of scientific knowledge becomes an unattainable ideal. One of the trends in the evolution of theoretical epistemology is the study of migration mechanisms of generation of scientific knowledge from the sphere of its own logic and methodology of science in the field of sociology - the consideration of this process, as the resulting system of interactions of social structures and institutions. Ensuing ideas and settings become the dominant worldview of philosophical and technological civilization. -/- . (shrink)

The vision of machines autonomously carrying out substantive conjecture generation, theorem discovery, proof discovery, and proof verification in mathematics and the natural sciences has a long history that reaches back before the development of automatic systems designed for such processes. While there has been considerable progress in proof verification in the formal sciences, for instance the Mizar project’ and the four-color theorem, now machine verified, there has been scant such work carried out in the realm of the natural (...) sciences—until recently. The delay in the case of the natural sciences can be attributed to both a lack of formal analysis of the so-called “theories” in such sciences, and the lack of sufficient progress in automated theorem proving. While the lack of analysis is probably due to an inclination toward informality and empiricism on the part of nearly all of the relevant scientists, the lack of progress is to be expected, given the computational hardness of automated theorem proving; after all, theoremhood in even first-order logic is Turing-undecidable. We give in the present short paper a compressed report on our building upon these formal theories using logic-based AI in order to achieve, in relativity, both machine proof discovery and proof verification, for theorems previously established by humans. Our report is intended to serve as a springboard to machine-produced results in the future that have not been obtained by humans. (shrink)

We investigate agents that have incomplete information and make decisions based on their beliefs expressed as situation calculus bounded action theories. Such theories have an infinite object domain, but the number of objects that belong to fluents at each time point is bounded by a given constant. Recently, it has been shown that verifying temporal properties over such theories is decidable. We take a first-person view and use the theory to capture what the agent believes about the domain of interest (...) and the actions affecting it. In this paper, we study verification of temporal properties over online executions. These are executions resulting from agents performing only actions that are feasible according to their beliefs. To do so, we first examine progression, which captures belief state update resulting from actions in the situation calculus. We show that, for bounded action theories, progression, and hence belief states, can always be represented as a bounded first-order logic theory. Then, based on this result, we prove decidability of temporal verification over online executions for bounded action theories. (shrink)

Vardi, M.Y., Verification of concurrent programs: the automata-theoretic framework, Annals of Pure and Applied Logic 51 79–98. We present an automata-theoretic framework to the verification of concurrent and nondeterministic programs. The basic idea is that to verify that a program P is correct one writes a program A that receives the computation of P as input and diverges only on incorrect computations of P. Now P is correct if and only if a program PA, obtained by combining (...) P and A, terminates. We formalize this idea in a framework of ω-automata with a recursive set of states. This unifies previous works on verification of fair termination and verification of temporal properties. (shrink)

The paper deals with the conception of logical empiricism developed by Eino Kaila. Eino Kaila, being a thinker close to the Vienna Circle, departs from some of the central ideas of logical positivism. He identifies a limited number of problems in metaphysics that are meaningful and need to be solved, but he declares the rest of metaphysics to be a logical fallacy. For Eino Kaila, it is not the principle of verification (as a criterion of meaning) but the principle (...) of testability that plays the most important role. In addition, he revises the principle of translatability, insisting that it is impossible to translate a single sentence into the language of experience, but it is possible to translate the whole theory to which the sentence belongs. This is related to his structuralist position in the philosophy of science and his understanding of scientific theories as ‘rationalisations’ as opposed to simple inductive generalisations. The paper compares Eino Kaila’s views expressed during the period of his active interaction with the Vienna Circle be regarded as a predecessor of later critics of logical positivism (in particular, W.V.O. Quine). (shrink)

(1) It remains to be seen if in the field of Psychiatry just as in that of Psychology the verbal output of a subject can be submitted to verification. Many statements of a highly emotional character being merely symptoms of certain dispositions have no direct communicative sense at all.(2) It being one of the characteristics of the mentally ill to loose contact and exchange of ideas with other people, the question naturally suggests itself if this symptom may be at (...) the bottom of the phenomenon of these persons taking refuge in logical and ideological terminologies, their talk being a kind of verbal autism. (shrink)

We study the existence of efficient approximation methods to verify quantitative specifications of probabilistic systems. Models of such systems are labelled discrete time Markov chains and checking specifications consists of computing satisfaction probabilities of linear temporal logic formulas. We prove that, in general, there is no polynomial time randomized approximation scheme with relative error for probabilistic verification. However, in many applications, specifications can be expressed by monotone formulas or negation of monotone formulas and randomized approximation schemes with absolute (...) error are sufficient. We show how some simple randomized approximation algorithms can improve the efficiency of verification of such probabilistic specifications and can be implemented in a probabilistic model checker. (shrink)

The world in which we find ourselves is religiously ambiguous. It is possible for different people to experience it both religiously and non-religiously; and to hold beliefs which arise from and feed into each of these ways of experiencing. A religious man may report that in moments of prayer he is conscious of existing in the unseen presence of God, and is aware - sometimes at least - that his whole life and the entire history of the world is taking (...) place within the ambience of the divine purpose. But on the other hand the majority of people in our modern world do not participate in that form of experience and are instead conscious of their own and others' lives as purely natural phenomena, so that their own experience leads them at least implicitly to reject the idea of a transcendent divine presence and purpose. If they are philosophically minded, they may well think that the believer's talk is the expression of what Richard Hare has called a blik , a way of feeling and thinking about the world which expresses itself in pseudo-assertions, pseudo because they are neither verifiable nor falsifiable and are therefore factually empty. 1 The religious man speaks of God as a living reality in whose presence we are, and of a divine purpose which gives ultimate meaning to our lives. But is not the world the same whether or not we suppose it to exist in God's presence; and is not the course of history the same whether or not we describe it as fulfilling God's purposes? Is not the religious description thus merely a gratuitous embellishment, a logical fifth wheel, an optional language-game which may assuage some psychological need of the speaker but which involves no claims of substance concerning the objective nature or structure of the universe? Must not the central religious use of language then be accounted a non-cognitive use, whose function is not to assert alleged facts but to express a speaker's, or a community of speakers', emotions within the framework of a factually contentless blik , ‘slant’, or ‘onlook’? (shrink)

In chapter VI of Language, Truth, and Logic, A.J. Ayer argues that ethical statements are not literally significant. Unlike metaphysical statements, however, ethical statements are not nonsensical: even though they are not literally significant, Ayer thinks that they possess some other sort of significance. This raises the question: by what principle or criterion can we distinguish, among the class of statements that are not literally significant, between those which are genuinely meaningless and those which possess some other, non-literal form (...) of significance. I suggest that Ayer needs a generalised version of the verification principle in order to answer this question. However, when we formulate the generalised version, it turns out that ethical statements do not satisfy it, so that the emotivist is committed to viewing ethics, like metaphysics, as meaningless verbiage. (shrink)

The article focuses on process management in public administration using the specific case study of the statutory city of Ostrava. Based on the selected part of the PAPRIS methodology, the process management is verified, and conclusions from the application of information system e-SMO are generalized. Ostrava is third the biggest city in Czech Republic with approximately 320 thousand citizen. Article describes experiences with SW implements, which are used for model of process in public administration. Particulary at local authority of Ostrava (...) town. Model of process is a basis for reengineering of process in state administration and preparation for implementation of big information systems. Mapping of process is providing implement and confirmation methodology to identify existing processes. Problem with its using consist in that, senior manager don’t informs, what organization is determination by processes. If are not described in given to organization current processes, or how would have had look new optimum processes, will not endeavour about reengineering successful. Procedural analysis namely offer tool and check methodology to identification current suit and it is possible him use either as instruction for reengineering function handling administrative and self-rule activities. Purpose of the article: The PAPRIS methodology was used when defining the objectives for implementation of the information system for public administration. This methodology has been elaborated by one of the authors and published in a very general scheme when solving many case studies,,. We assume that the PAPRIS is primarily a methodology with incorporated elements of procedural approach for project management in public administration information systems. The specific supporting process of communication between the client and the e-SMO system has been chosen for verification. The model of supporting communication process, created by ARIS tools, is crucial, and the structure of scripts is subsequently made. The aim of this article is to verify that the methodology is sufficient and appropriate to manage such a large project such, undoubtedly, is the e-SMO. Methodology/methods: Defined productive and non-productive processes with their defined process cuts represent a crucial category for the process structure of IS projects. This is fully accepted by the PAPRIS methodology. Process cuts are understood, in the logic modelling according to the PAPRIS methodology, as clearly defined logic directional cuts in three-dimensional space of all project processes. The process set is systemically categorized, in a given logic directional cut, into mutually disjoint process subsets, which are characterized by this particular directional operator. The directional operator always has a clear logical allocation that is based on the construction of a process view. Theoretically, an infinite number of process views can be used. One of the important issues in a methodology for the case studies includes the size of the research sample. It is usually assumed that there is no ideal number of cases and that the number between four and ten usually provides good results. Other authors defining against any quantitative standards for any determination of the sample size of the case studies, since such an approach denies the internal logic of this methodology and the richness of the information obtained from participants in the research. Research which is carried out using case studies does not aspire on compliance with the requirement the representativeness of the sample.. Methodology of case studies is among the established guidelines of qualitative research. Research on using case studies in the last 30 years has seen an extraordinary increase in social-scientific research, including research on business and management. Scientific aim: The essential aim of this study is to describe the way the process cut defines a productive process and non-productive process, in accordance with the PAPRIS methodology using the specific example. While the triggering mechanism of the project production process is an event causing its own production - i.e. the specific output with added value for the customer, the project of non-productive process is caused by the project management event. Therefore, it is caused by the need to control, monitor, track, inspect, evaluate outputs, decide and regulate the project implementation. Findings: Within the support of the communication process, two examples were used to verify the methodology. The global perspective on the process was created in ARIS tools and the communication between the call centre and the client was made in Visio tools. The PAPRIS methodology is based on the concept of process variability, which has been clearly formulated. The fundamental direction of the process development, anticipated changes and the opportunity to react to them in accordance with defined objectives of the PAIS project are guaranteed. (shrink)

Quantum logic as genuine non-classical logic provides no solution to the "paradoxes" of quantum mechanics. From the minimal condition that synonyms be substitutable salva veritate, it follows that synonymous sentential connectives be alike in point of truth-functionality. It is a fact of pure mathematics that any assignment Φ of (0, 1) to the subspaces of Hilbert space (dim. ≥ 3) which guarantees truth-preservation of the ordering and truth-functionality of QL negation, violates truth-functionality of QL ∨ and $\wedge $ (...) . Thus, from within both the classical framework and that of any QL that preserves elementary set theory, two distinct (nonsynonymous) sets of connectives are discernible. Classical derivations of QM paradoxes are all available unless the language of QM is not classically closed. Maintaining this requires a strong and selfdefeating verification theory of meaning, the philosophical cornerstone of the Copenhagen interpretation to which QL was to provide an alternative. (shrink)

Kotek et al. argue on the basis of novel experimental evidence that sentences like ‘Most of the dots are blue’ are ambiguous, i.e. have two distinct truth conditions. Kotek et al. furthermore suggest that when their results are taken together with those of earlier work by Lidz et al., the overall picture that emerges casts doubt on the conclusions that Lidz et al. drew from their earlier results. We disagree with this characterization of the relationship between the two studies. Our (...) main aim in this reply is to clarify the relationship as we see it. In our view, Kotek et al.’s central claims are simply logically independent of those of Lidz et al.: the former concern which truth condition a certain kind of sentence has, while the latter concern the procedures that speakers choose for the purposes of determining whether a particular truth condition is satisfied in various scenes. The appearance of a conflict between the two studies stems from inattention to the distinction between questions about truth conditions and questions about verification procedures. (shrink)

Burge follows Descartes in claiming that the category of conceptually self-verifying judgments includes (but is not restricted to) judgments that give rise to sincere assertions of sentences of the form, 'I am thinking that p'. In this paper I argue that Burge’s Cartesian insight is hard to reconcile with Fregean accounts of the content of thought. Burge's intuitively compelling claim that cogito judgments are conceptually self-verifying poses a real challenge to neo-Fregean theories of content.

Descartes famously argued, on purely conceptual grounds, that even an extremely powerful being could not trick him into mistakenly judging that he was thinking. Of course, it is not necessarily true that Descartes is thinking. Still, Descartes claimed, it is necessarily true that if a person judges that she is thinking, that person is thinking. Following Tyler Burge (1988) we call such judgments ‘self-verifying.’ More exactly, a judgment j performed by a subject S at a time t is selfverifying if (...) and only if the fact that S has made j at t entails that j is true at t.2 Burge follows Descartes in claiming that the category of conceptually self-verifying judgments includes (but is not restricted to) judgments that give rise to sincere assertions of sentences of the form, ‘I am thinking that p’. We call such judgments ‘cogito’ judgments. In this paper I argue that Burge’s Cartesian insight is hard to reconcile with Fregean accounts of the content of thought. Theorists have tried to account for the self-verifying status of cogito judgments by arguing that the second-order judgment that one is thinking that p contains the thought that p as a part of it. I argue (§1) that the accuracy of the containment model is entailed by a Russellian view of content (according to which ‘‘belief’’ contexts are both extensional and transparent) when the Russellian view is attached to some fairly uncontroversial assumptions. The accuracy of the containment model is also entailed by non-hierarchical Fregean views of content according to which expressions in oblique contexts both denote and express first-level senses (§2), but there are compelling arguments against non-hierarchical Fregean views (§3). Moreover, the extremely plausible account of self-verification provided by Russellianism is not entailed by theories that follow Frege in accepting a hierarchy of senses and so allow that expressions in oblique contexts express senses that are not identical to the senses they there denote (§4).. (shrink)

Various four- and three-valued modal propositional logics are studied. The basic systems are modal extensions BK and BS4 of Belnap and Dunn's four-valued logic of firstdegree entailment. Three-valued extensions of BK and BS4 are considered as well. These logics are introduced semantically by means of relational models with two distinct evaluation relations, one for verification and the other for falsification. Axiom systems are defined and shown to be sound and complete with respect to the relational semantics and with (...) respect to twist structures over modal algebras. Sound and complete tableau calculi are presented as well. Moreover, a number of constructive non-modal logics with strong negation are faithfully embedded into BS4, into its three-valued extension B3S4, or into temporal BS4, BtS4. These logics include David Nelson's three-valued logic N3, the four-valued logic N4 bottom, the connexive logic C, and several extensions of bi-intuitionistic logic by strong negation. (shrink)

We present a technique for automatically verifying cryptographic protocols specified in the mainstream specification language CAPSL. We define a translation from CAPSL models into interpreted systems, a popular semantics for temporal-epistemic logic, and rewrite CAPSL goals as temporal-epistemic specifications. We present a compiler that implements this translation. The compiler links to the symbolic model checker MCMAS. We evaluate the technique on protocols in the Clark-Jacobs library and in the SPORE repository against custom secrecy and authentication requirements.

The value of logic techniques in circuit design has been well-known for many years, but a thorough grounding in mathematical logic is needed for all stages of software development, especially program specification, verification and program transformation. In all these stages, logic underpins the theory, bearing out the dictum that Logic is the calculus of computer science. This book presents the subject of mathematical logic in order to provide a grounding for students in computer science.

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, (...) but have been expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

The main result of this paper is that KT is closed under a cancellation principle. This result extends to KTG1, but it does not extend to modal systems associated with the provability interpretation of L, such as KW and KT4Grz. Following Williamson, these results are applied to philosophical concerns about the proper form for theories of meaning, via the interpretation of L as some kind of veriflability. The cancellation principle can then be read as saying that verifilability conditions and falsiflability (...) conditions jointly determine truth conditions. (shrink)

An understanding of logic is essential to computer science. This book provides a highly accessible account of the logical basis required for reasoning about computer programs and applying logic in fields like artificial intelligence. The text contains extended examples, algorithms, and programs written in Standard ML and Prolog. No prior knowledge of either language is required. The book contains a clear account of classical first-order logic, one of the basic tools for program verification, as well as (...) an introductory survey of modal and temporal logics and possible world semantics. An introduction to intuitionistic logic as a basis for an important style of program specification is also featured in the book. (shrink)

Abstract This article examines the little-explored remarks on verification in Wittgenstein's notebooks during the period between 1930 and 1932. In these remarks, Wittgenstein connects a verificationist theory of meaning with the notion of logical multiplicity, understood as a space of possibilities: a proposition is verified by a fact if and only if the proposition and the fact have the same logical multiplicity. But while in his early philosophy logical multiplicities were analysed as an outcome of the formal properties of (...) simple objects and simple signs, Wittgenstein in the early 1930s connects the notion of logical multiplicity with the notion of ways of seeing. I will argue that the relevant ways of seeing are closely similar to seeing-as or aspect seeing. According to Wittgenstein's view in the early 1930s, logical multiplicities are part of our perceptual experience of propositions and facts. In this sense, the verification relation depends on how we experience propositions and facts as being surrounded by a logical space of possibilities. Strikingly, Wittgenstein's way of thinking about the verification relation offers solutions to a set of seemingly intractable problems connected with the versions of verificationism developed by members of the Vienna Circle. (shrink)

Security properties naturally combine temporal aspects of protocols with aspects of knowledge of the agents. Since BAN-logic, there have been several initiatives and attempts to incorpórate epistemics into the analysis of security protocols. In this paper, we give an overview of work in the field and present it in a unified perspective, with comparisons on technical subtleties that have been employed in different approaches. Also, we study to which degree the use of epistemics is essential for the analysis of (...) security protocols. We look for formal conditions under which knowledge modalities can bring extra expressive power to pure temporal languages. On the other hand, we discuss the cost of the epistemic operators in terms of model checking complexity. (shrink)

Fetzer famously claims that program verification is not even a theoretical possibility, and offers a certain argument for this far-reaching claim. Unfortunately for Fetzer, and like-minded thinkers, this position-argument pair, while based on a seminal insight that program verification, despite its Platonic proof-theoretic airs, is plagued by the inevitable unreliability of messy, real-world causation, is demonstrably self-refuting. As I soon show, Fetzer is like the person who claims: ‘My sole claim is that every claim expressed by an English (...) sentence and starting with the phrase “My sole claim” is false’. Or, more accurately, such thinkers are like the person who claims that modus tollens is invalid, and supports this claim by giving an argument that itself employs this rule of inference. (shrink)

A. J. Ayer’s empiricist criterion of meaning was supposed to have sorted all statements into nonsense on the one hand, and tautologies or genuinely factual statements on the other. Unfortunately for Ayer, it follows from classical logic that his criterion is trivial—it classifies all statements as either tautologies or genuinely factual, but none as nonsense. However, in this paper, I argue that Ayer’s criterion of meaning can be defended from classical proofs of its triviality by the adoption of a (...) relevant logic—an idea which is motivated because, according to Ayer, the genuinely factual statements are those which observation is relevant to. (shrink)

This book is a compact, accessible treatment of the main ideas advanced by the positivists, including Schlick, Carnap, Ayer, and the early Wittgenstein. Oswald Hanfling discusses such ideas as the 'verification principle' ('the meaning of this statement is the method of its verification') and the 'elimination of metaphysics, ' an attempt to show that metaphysical statements, for example about God, are unverifiable and therefore meaningless.

We propose a logic for reasoning about metric spaces with the induced topologies. It combines the ‘qualitative’ interior and closure operators with ‘quantitative’ operators ‘somewhere in the sphere of radiusr’ including or excluding the boundary. We supply the logic with both the intended metric space semantics and a natural relational semantics, and show that the latter (i) provides finite partial representations of (in general) infinite metric models and (ii) reduces the standard ‘ε-definitions’ of closure and interior to simple (...) constraints on relations. These features of the relational semantics suggest a finite axiomatisation of the logic and provide means to prove its EXPTIME-completeness (even if the rational numerical parameters are coded in binary). An extension with metric variables satisfying linear rational (in)equalities is proved to be decidable as well. Our logic can be regarded as a ‘well-behaved’ common denominator of logical systems constructed in temporal, spatial, and similarity-based quantitative and qualitative representation and reasoning. Interpreted on the real line (with its Euclidean metric), it is a natural fragment of decidable temporal logics for specification and verification of real-time systems. On the real plane, it is closely related to quantitative and qualitative formalisms for spatial representation and reasoning, but this time the logic becomes undecidable. (shrink)