Game semantics

We introduce model-checking games that allow local second-order power on sets of independent transitions in the underlying partial order models where the games are played. Since the interleaving semantics of such models is not considered, some problems that may arise when using interleaving representations are avoided and new decidability results for partial order models are achieved. The games are shown to be sound and complete, and therefore determined. While in the interleaving case they coincide with the local model-checking games for the µ-calculus, in a partial order setting they verify properties of a number of fixpoint modal logics that can specify in concurrent systems with partial order semantics, several properties not expressible with the µ-calculus. The games underpin a novel decision procedure for model-checking all temporal properties of a class of infinite and regular event structures, thus improving previous results in the literature.

We show that the karoubian envelope of the category of correspondances is equivalent to the category of sup-compatible mappings between complete completly distributive lattices. On sait que l’enveloppe karoubienne per met de ramener les notions semi-fonctor ielles à des notions fonctorielles, et en particulier produit des catégories car tésiennes fer mées à partir de catégories faiblement cartésiennes fermées, ce qui est utilisé en théorie des dolnaines pour obtenir des modèles de la logique linéaire. Voir [2], [3]. On sait aussi que la modélisation et la manipulation algébrique de systèmes informatiques fait appel à des correspondances de Galois analysables et génér alisables en termes de transversalité de correspondances difonctionnelles. Voir [9]. Enfin on sait que Raney a établi un lien étroit entre les "tight" correspondances de Galois et les treillis co1plètement distributifs, qui sont des treillis continus particuliers. Voir [5, 6, 7] et [1]. Le lien entre ces diver...

Blass, A., A game semantics for linear logic, Annals of Pure and Applied Logic 56 (1992) 183-220. We present a game (or dialogue) semantics in the style of Lorenzen (1959) for Girard's linear logic (1987). Lorenzen suggested that the (constructive) meaning of a proposition 91 should be specified by telling how to conduct a debate between a proponent P who asserts p and an opponent 0 who denies q. Thus propositions are interpreted as games, connectives (almost) as operations on games, and validity as existence of a winning strategy for P. (The qualifier 'almost' will be discussed later when more details have been presented.) We propose that the connectives of linear logic can be naturally interpreted as the operations on games introduced for entirely different purposes by Blass (1972). We show that affine logic, i.e., linear logic plus the rule of weakening, is sound for this interpretation. We also obtain a completeness theorem for the additive fragment of affine logic, but we show that completeness fails for the multiplicative fragment. On the other hand, for the multiplicative fragment, we obtain a simple characterization of game-semantical validity in terms of classical tautologies. An analysis of the failure of completeness for the multiplicative fragment leads to the conclusion that the game interpretation of the connective @ is weaker than the interpretation implicit in Girard's proof rules; we discuss the differences between the two interpretations and their relative advantages and disadvantages. Finally, we discuss how Godel's Dialectica interpretation (1958), which was connected to linear logic by de Paiva (1989) fits with game semantics.

Although aware of making a striking statement, it can be argued that there has never been—with minor exceptions—a genuinely Kantian account of Kant’s Philosophy of Mathematics. As Robert Brandom noted, the epistemic premise of Kantian epistemology is not some sort of grounding. Instead, the possibility of knowledge is already guaranteed by the fact that true and false are given in our cognitive practices; if knowledge were not possible, the very concept of falsehood would not exist.
However, today the two major interpretations of synthetic a priori judgements can be traced back historically to Russell and Cassirer. Whilst they disagree on the validity of Kant’s point, both interpretations see Pure Intuition as drawing from some imaginary epistemic foundation. Such a premise is not Kantian but rather Cartesian in nature and has the effect ruling out the possibility of a truly Kantian take on Logic, in Russell out of contempt, in Cassirer out of haughtiness. Based on these observations, we can re-evaluate Hintikka's work on Kant's mathematical theory—which had been criticised precisely for its greatest merit i.e. not having an epistemic foundation—as the groundwork for a truly Kantian Philosophy of Mathematics.

We rene Gentzen's classical sequent calculus into a classical tableau calculus within the framework of Martin-Lof's type theory. This cal-culus has essentially the same inference gures as Gentzen's classical sequent calculus, but there are two important departures from the lat-ter: there are no structural inference gures except cut, and categories in the sense of Martin-Lof's type theory replace sequents. The classical tableau calculus admits a normalization algorithm similar to the algorithm implicit in Gentzen's Hauptsatz, however con-uent and strongly normalizing. The proof of the latter conforms with Gandy's technique, which in turn relies on the algorithm being weakly normalizing, here proved along the same line of argument as Gentzen's Hauptsatz. 1

Efficiency of asynchronous optimistic fair exchange using trusted devices is studied. It is shown that three messages in the optimistic subprotocol are sufficient and necessary for exchanging idempotent items. When exchanging nonidempotent items, however, three messages in the optimistic subprotocol are sufficient only under the assumption that trusted devices have unbounded storage capacity. This assumption is often not satisfiable in practice. It is then proved that exchanging nonidempotent items using trusted devices with a bounded storage capacity requires exactly four messages in the optimistic subprotocol.

In this paper, we generalize modal µ-calculus to the nondistributive (lattice-based) modal µ-calculus and formalize some scenarios regarding categorization using it. We also provide a game semantics for the developed logic. The proof of adequacy of this game semantics proceeds by generalizing the unfolding games on the power-set algebras to the arbitrary lattices and showing that these games can be used to determine the least and the greatest fixed points of a monotone operator on a lattice. Finally, we define a notion of bisimulations on the polarities and show invariance of non-distributive modal µ-calculus under them.

We present an infinite-game characterization of the well-founded semantics for function-free logic programs with negation. Our game is a simple generalization of the standard game for negation-less logic programs introduced by M.H. van Emden (1986, Journal of Logic Programming, 3(1), 37-53) in which two players, the Believer and the Doubter, compete by trying to prove (respectively disprove) a query. The standard game is equivalent to the minimum Herbrand model semantics of logic programming in the sense that a query succeeds in the minimum model semantics iff the Believer has a winning strategy for the game which begins with the Doubter doubting this query. The game for programs with negation that we propose follows the same rules as the standard one, except that the players swap roles every time the play "passes through" negation. We start our investigation by establishing the determinacy of the new game by using some classical tools from the theory of infinite-games. Our determinacy result immediately provides a novel and purely game-theoretic characterization of the semantics of negation in logic programming. We proceed to establish the connections of the game semantics to the existing semantic approaches for logic programming with negation. For this purpose, we first define a refined version of the game that uses degrees of winning and losing for the two players. We then demonstrate that this refined game corresponds exactly to the infinite-valued minimum model semantics of negation (Rondogiannis & Wadge, 2005, ACM TOCL, 6(2), 441-467). This immediately implies that the unrefined game is equivalent to the well-founded semantics (since the infinite-valued semantics is a refinement of the well-founded semantics).

We introduce a notion of strong monotonicity of probabilistic predicate transformers. This notion enables us to establish a normal form theorem for monotone probabilistic predicate transformers. Three other healthiness conditions, namely, conjunctivity, disjunctivity and continuity for probabilistic predicate transformers are also examined, and they are linked to strong monotonicity. A notion of probabilistic refinement index is proposed, and it provides us with a continuous strength spectrum of refinement relations which may be used to describe more flexible refinement between probabilistic programs. A notion of probabilistic correctness is introduced too. We give a probabilistic weakest-precondition, choice and game semantics to the contract language, and present a probabilistic generalization of the winning strategy theorem.

Simulation and bisimulation metrics for stochastic systems provide a quantitative generalization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative specifications written in the quantitative µ-calculus and related probabilistic logics. We first show that the metrics provide a bound for the difference in long-run average and discounted average behavior across states, indicating that the metrics can be used both in system verification, and in performance evaluation. For turn-based games and MDPs, we provide a polynomial-time algorithm for the computation of the one-step metric distance between states. The algorithm is based on linear programming; it improves on the previous known exponential-time algorithm based on a reduction to the theory of reals. We then present PSPACE algorithms for both the decision problem and the problem of approximating the metric distance between two states, matching the best known algorithms for Markov chains. For the bisimulation kernel of the metric our algorithm works in time O(n 4) for both turn-based games and MDPs; improving the previously best known O(n 9 • log(n)) time algorithm for MDPs. For a concurrent game G, we show that computing the exact distance between states is at least as hard as computing the value of concurrent reachability games and the squareroot-sum problem in computational geometry. We show that checking whether the metric distance is bounded by a rational r, can be done via a reduction to the theory of real closed fields, involving a formula with three quantifier alternations, yielding O(|G| O(|G| 5)) time complexity, improving the previously known reduction, which yielded O(|G| O(|G| 7)) time complexity. These algorithms can be iterated to approximate the metrics using binary search.

Simulation and bisimulation metrics for stochastic systems provide a quantitative generalization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative specifications written in the quantitative {\mu}-calculus and related probabilistic logics. We first show that the metrics provide a bound for the difference in long-run average and discounted average behavior across states, indicating that the metrics can be used both in system verification, and in performance evaluation. For turn-based games and MDPs, we provide a polynomial-time algorithm for the computation of the one-step metric distance between states. The algorithm is based on linear programming; it improves on the previous known exponential-time algorithm based on a reduction to the theory of reals. We then present PSPACE algorithms for both the decision problem and the problem of approximating the metric distance between two states, matching the bes...

We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose probability distributions over moves, rather than single moves. Given a goal, for example, reach a target state, the question of winning is thus a probabilistic one: what is the maximal probability of winning from a given state? On these game structures, two fundamental notions are those of equivalences and metrics. Given a set of winning conditions, two states are equivalent if the players can win the same games with the same probability from both states. Metrics provide a bound on the difference in the probabilities of winning across states, capturing a quantitative notion of state similarity. We introduce equivalences and metrics for two-player game structures, and we show that they characterize the difference in probability of winning games whose...

Bounded linear types have proved to be useful for automated resource analysis and control in functional programming languages. In this paper we introduce an affine bounded linear typing discipline on a general notion of resource which can be modeled in a semiring. For this type system we provide both a general type-inference procedure, parameterized by the decision procedure of the semiring equational theory, and a (coherent) categorical semantics. This is a very useful type-theoretic and denotational framework for many applications to resourcesensitive compilation, and it represents a generalization of several existing type systems. As a non-trivial instance, motivated by our ongoing work on hardware compilation, we present a complex new application to calculating and controlling timing of execution in a (recursion-free) higher-order functional programming language with local store.

This paper extends previous work on the compilation of higher-order imperative languages into digital circuits [4]. We introduce concurrency, an essential feature in the context of hardware compilation and we re-use an existing game model to simplify correctness proofs. The target designs we compile to are asynchronous event-logic circuits, which naturally match the asynchronous game model of the language.

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Design of geotechnical systems is often challenging as it requires the understanding of complex soil behaviour and its influence on field-scale performance of geo-structures. To advance the scientific knowledge and the technological development in geotechnical engineering, a Scottish academic community, named Scottish Universities Geotechnics Network (SUGN), was established in 2001, composing of eight higher education institutions. The network gathers geotechnics researchers, including experimentalists as well as centrifuge, constitutive, and numerical modellers, to generate multiple synergies for building larger collaboration and wider research dissemination in and beyond Scotland. The paper will highlight the research excellence and leading work undertaken in SUGN emphasising some of the contribution to the geotechnical research community and some of the significant research outcomes.

Design of geotechnical systems is often challenging as it requires the understanding of complex soil behaviour and its influence on field-scale performance of geo-structures. To advance the scientific knowledge and the technological development in geotechnical engineering, a Scottish academic community, named Scottish Universities Geotechnics Network (SUGN), was established in 2001, composing of eight higher education institutions. The network gathers geotechnics researchers, including experimentalists as well as centrifuge, constitutive, and numerical modellers, to generate multiple synergies for building larger collaboration and wider research dissemination in and beyond Scotland. The paper will highlight the research excellence and leading work undertaken in SUGN emphasising some of the contribution to the geotechnical research community and some of the significant research outcomes.

An intensional model for the programming language PCF is described in which the types of PCF are interpreted by games and the terms by certain history-free strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable in a certain simple extension of PCF. We then introduce an intrinsic preorder on strategies and show that it satisfies some striking properties such that the intrinsic preorder on function types coincides with the pointwise preorder. We then obtain an order-extensional fully abstract model of PCF by quotienting the intensional model by the intrinsic preorder. This is the first syntax-independent description of the fully abstract model for PCF. (Hyland and Ong have obtained very similar results by a somewhat different route, independently and at the same time.) We then consider the effective version of our model and prove a universality theorem: every element of the effective extensional model is definable in PCF. Equivalently, every recursive strategy is definable up to observational equivalence.

We present the web portal Λ-symsym, available at http://158.110.146.197:31780/automata/, for experimenting with game semantics of λ !-calculus, and its normalizing elementary sub-calculus, the λ EAL-calculus. The λ !-calculus is a generalization of the λ-calculus obtained by introducing a modal operator !, giving rise to a pattern β-reduction. Its sub-calculus corresponds to an applicatively closed class of terms normalizing in an elementary number of steps, in which all elementary functions can be encoded. The game model which we consider is the Geometry of Interaction model I introduced by Abramsky to study reversible computations, consisting of partial involutions over a very simple language of moves. Given a λ !-or a λ EAL-term, M , Λ-symsym provides: an abstraction algorithm A ! , for compiling M into a term, A ! (M), of the linear combinatory logic CL ! , or the normalizing combinatory logic CL EAL ; an interpretation algorithm [[ ]] I yielding a specification of the partial involution [[A ! (M)]] I in the model I; an algorithm, I2T , for synthesizing from [[A ! (M)]] I a type, I2T ([[A ! (M)]] I), in a multimodal, intersection type assignment discipline, ⊢ !. an algorithm, T 2I, for synthesizing a specification of a partial involution from a type in ⊢ ! , which is an inverse to the former. We conjecture that ⊢ ! M : I2T ([[A ! (M)]] I). Λ-symsym permits to investigate experimentally the fine structure of I, and hence the game semantics of the λ !-and λ EAL-calculi. For instance, we can easily verify that the model I is a λ !-algebra in the case of strictly linear λ-terms, by checking all the necessary equations, and find counterexamples in the general case. We make this tool available for readers interested to play with games (-semantics). The paper builds on earlier work by the authors, the type system being an improvement.

Joyal's categorical construction on (well-founded) Conway games and winning strategies provides a compact closed category, where tensor and linear implication are defined via Conway disjunctive sum (in combination with negation for linear implication). The equivalence induced on games by the morphisms coincides with the contextual closure of the equideterminacy relation w.r.t. the disjunctive sum. Recently, the above categorical construction has been generalized to non-wellfounded games. Here we investigate Joyal's construction for a different notion of sum, i.e. selective sum. While disjunctive sum reflects the interleaving semantics, selective sum accommodates a form of parallelism, by allowing the current player to move in different parts of the board simultaneously. We show that Joyal's categorical construction can be successfully extended to selective sum, when we consider alternating games, i.e. games where each position is marked as Left player (L) or Right player (R), that is only L or R can move from that position, R starts, and L/R positions strictly alternate. Alternating games typically arise in the context of Game Semantics. This category of well-founded games with selective sum is symmetric monoidal closed, and it induces exactly the equideterminacy relation. Generalizations to non-wellfounded games give linear categories, i.e. models of Linear Logic. Our game models, providing a certain level of parallelism, may be situated halfway between traditional sequential alternating game models and the concurrent game models by Abramsky and Mellies. We work in a context of coalgebraic games, whereby games are viewed as elements of a final coalgebra, and game operations are defined as final morphisms.

Joyal's categorical construction on (well-founded) Conway games and winning strategies provides a compact closed category, where tensor and linear implication are defined via Conway disjunctive sum (in combination with negation for linear implication). The equivalence induced on games by the morphisms coincides with the contextual closure of the equideterminacy relation w.r.t. the disjunctive sum. Recently, the above categorical construction has been generalized to non-wellfounded games. Here we investigate Joyal's construction for a different notion of sum, i.e. selective sum. While disjunctive sum reflects the interleaving semantics, selective sum accommodates a form of parallelism, by allowing the current player to move in different parts of the board simultaneously. We show that Joyal's categorical construction can be successfully extended to selective sum, when we consider alternating games, i.e. games where each position is marked as Left player (L) or Right player (R), that is only L or R can move from that position, R starts, and L/R positions strictly alternate. Alternating games typically arise in the context of Game Semantics. This category of well-founded games with selective sum is symmetric monoidal closed, and it induces exactly the equideterminacy relation. Generalizations to non-wellfounded games give linear categories, i.e. models of Linear Logic. Our game models, providing a certain level of parallelism, may be situated halfway between traditional sequential alternating game models and the concurrent game models by Abramsky and Mellies. We work in a context of coalgebraic games, whereby games are viewed as elements of a final coalgebra, and game operations are defined as final morphisms.

The newly emerging branch of research of Computer Science received encouragement from the successors of the Warsaw mathematical school: Kuratowski, Mazur, Mostowski, Grzegorczyk, and Rasiowa. Rasiowa realized very early that the spectrum of computer programs should be incorporated into the realm of mathematical logic in order to make a rigorous treatment of program correctness. This gave rise to the concept of algorithmic logic developed since the 1970s by Rasiowa, Salwicki, Mirkowska, and their followers. Together with Pratt's dynamic logic, algorithmic logic evolved into a mainstream branch of research: logic of programs. In the late 1980s, Warsaw logicians Tiuryn and Urzyczyn categorized various logics of programs, depending on the class of programs involved. Quite unexpectedly, they discovered that some persistent open questions about the expressive power of logics are equivalent to famous open problems in complexity theory. This, along with parallel discoveries by Harel, Immerman and Vardi, contributed to the creation of an important area of theoretical computer science: descriptive complexity. By that time, the modal µ-calculus was recognized as a sort of a universal logic of programs. The mid 1990s saw a landmark result by Walukiewicz, who showed completeness of a natural axiomatization for the µ-calculus proposed by Kozen. The difficult proof of this result, based on automata theory, opened a path to further investigations. Later, Bojanczyk opened a new chapter by introducing an unboundedness quantifier, which allowed for expressing some quantitative properties of programs. Yet another topic, linking the past with the future, is the subject of automata founded in the Fraenkel-Mostowski set theory. The studies on intuitionism found their continuation in the studies of Curry-Howard isomorphism. Łukasiewicz's landmark idea of many-valued logic found its continuation in various approaches to incompleteness and uncertainty.

We present a game model of the untyped-calculus, with equational theory equal to the B ohm tree-theory B, which is universal (i.e. every element of the model is deÿnable by some term). This answers a question of Di Gianantonio, Franco and Honsell. We build on our earlier work, which uses the methods of innocent game semantics to develop a universal model inducing the maximal consistent sensible theory H *. To our knowledge these are the ÿrst syntax-independent universal models of the untyped-calculus.

We present a game model of the untyped-calculus, with equational theory equal to the B ohm tree-theory B, which is universal (i.e. every element of the model is deÿnable by some term). This answers a question of Di Gianantonio, Franco and Honsell. We build on our earlier work, which uses the methods of innocent game semantics to develop a universal model inducing the maximal consistent sensible theory H *. To our knowledge these are the ÿrst syntax-independent universal models of the untyped-calculus.

In some business areas there is the need to use representations of places or buildings in order to provide visual informations. These representations are, mainly, reconstructions of scaled real models or virtual representations produced in a Computer-Aided Design (CAD) tool. Recently, procedural modeling has been applied to generate buildings and cities in a short time and with a minimum user intervention. This methodology reveals to be a promising solution for a costeffective alternative in models construction. One of the areas that can benefit from this kind of approach is archeology, for example to test archeological hypothesis. However, the existing solutions are not flexible enough to provide high detailed models containing building interiors and exteriors. This paper aims to present the global architecture and specification of an information system that supports the procedural modeling process, producing enhanced virtual representations of ancient places, including building facades and interiors, using the information available.

There is a robust debate on different linguistic levels of quantifier ambiguity resolution. Many accounts of the quantifier ambiguity are extensively examined in Turkish by semantic-prosodic and syntactic-semantic levels in previous studies. In this study, we aimed to investigate the prosodic and syntactic processes of the universal quantifier (her (‘every’) and existential quantifier bir (‘a/an’)) by using an on-line picture matching experiment with 75 young adults and native speakers of Turkish. Our stimuli consisted of 120 sentences (30×4) for each of the conditions with order (her–bir (‘every–a/an’) vs. bir–her ‘a/an–every’) × focus (subject position vs. object position), respectively. In each trial, participants were asked to listen to the auditory stimuli and to judge sentences they heard. Our findings showed that the focused existential quantifier bir (‘a/an’) assigned wider scope than the universal quantifier her (‘every’) for the judgment task rates. This finding suggested ...

We show that Hyland and Ong's game semantics for PCF can be presented using normalization by evaluation (nbe). We use the bijective correspondence between innocent well-bracketed strategies and PCF Böhm trees, and show how operations on PCF Böhm trees, such as composition, can be computed lazily and simply by nbe. The usual equations characteristic of games follow from the nbe construction without reference to low-level game-theoretic machinery. As an illustration, we give a Haskell program computing the application of innocent strategies.

The Barth-Krabbe-Hintikka-Hintikka Problem, independently raised by Barth and Krabbe (From axiom to dialogue: a philosophical study of logics and argumentation. Walter de Gruyter, Berlin, 1982) and Hintikka and Hintikka (The sign of three: Peirce, Dupin, Holmes. In: Eco U, Sebeok TA (eds) Sherlock Holmes confronts modern logic: Toward a theory of information-seeking through questioning. Indiana University Press, Bloomington, 1983), is the problem of characterizing the strategic reasoning of the players of dialogical logic and game-theoretic semantics games from rational preferences rather than rules. We solve the problem by providing a set of preferences for players with bounded rationality and specifying strategic inferences from those preferences, for a variant of logical dialogues. This solution is generalized to both game-theoretic semantics and orthodox dialogical logic (classical and intuitionistic).

In this paper we consider the problem of deriving a term assignment system for Girard's Intuitionistic Linear Logic for both the sequent calculus and natural deduction proof systems. Our system di ers from previous calculi (e.g. that of Abramsky) and has two important properties which they lack. These are the substitution property (the set of valid deductions is closed under substitution) and subject reduction (reduction on terms is well-typed). We de ne a simple (but more general than previous proposals) categorical model for Intuitionistic Linear Logic and show how this can be used to derive the term assignment system. We also consider term reduction arising from cut-elimination in the sequent calculus and normalisation in natural deduction. We explore the relationship between these, as well as with the equations which follow from our categorical model.

We present a mathematical model which is the most abstract allowing (i) a fully compositional semantics for timed CSP and (ii) a natural abstraction map into the standard failures/divergences model of untimed CSP. We discuss the construction and properties of this model and ways in which it can be used to give semantics to CSP reflecting several implementation strategies.

Formalizing and verifying proofs in cryptography has become an important task. Backes et al. therefore invented a framework [1] that uses the proof assistant Isabelle/HOL [9] to verify game-based proofs. In this framework a powerful probabilistic language allows to formalize games that describe security properties. To show that these security properties hold one can modify the games such that their outcome is not altered. This is done until the games have the form of already known security properties. Such a modification of a game is called a transformation. Transformations are based on relations between games which have to be verified. But verifying such relations is very often a challenging task. To be able to come up with game-based proofs more naturally it is useful to have a collection of relations, and therefore transformations, verified upfront. This thesis presents a couple of different game-transformations, formalizes them, and shows proofs of their correctness.

In this paper we consider parity games defined by higher-order pushdown automata. These automata generalise pushdown automata by the use of higher-order stacks, which are nested "stack of stacks" structures. Representing higher-order stacks as well-bracketed words in the usual way, we show that the winning regions of these games are regular sets of words. Moreover a finite automaton recognising this region can be effectively computed. A novelty of our work are abstract pushdown processes which can be seen as (ordinary) pushdown automata but with an infinite stack alphabet. We use the device to give a uniform presentation of our results. From our main result on winning regions of parity games we derive a solution to the Modal Mu-Calculus Global Model-Checking Problem for higher-order pushdown graphs as well as for ranked trees generated by higher-order safe recursion schemes. * We direct readers to the (downloadable) long version [11] of this paper in which all proofs are presented.

W e present a novel conjecture concerning the scope ambiguities that arise in sentences including multiple non-referential quantifiers. W e claim that many existing theories of the phenomenon fail to correctly limit the set of readings that such sentences engender by failing to distinguish between referential and non-referential quantifiers. Once the distinction is correctly drawn, we show that surface syntax can be made, via an extended notion of surface constituency, to identify the set of available diflerently-scoped readings for such sentences. We examine various English constructions to show that the scopings predicted by the conjecture are the only ones that are available to human language understanders. W e show how to incorporate this conjecture into a theory of quantifier scope, by couching it in a unification-based Combinatory Categorial Grammar framework and implementing it in SICStus Prolog. Finally, we compare the proposal with related approaches to quantifier scope ambiguity.

The last half-century has witnessed a resurgence of interest in Aristotle's Topics and his theory of dialectic-culminating in J. D. G. Evan's book about Aristotle's concept of dialectic; the decision to devote the entire Third Symposium Aristotelicum to the Topics; and the appearance of a small but steady stream of articles, several of which are now conveniently bound together in the first volume of Articles on Aristotle, edited by Barnes, Schofield, and Sorabji. 1 These studies provide two somewhat incompatible views of Aristotle's dialectic. On the one hand, it is argued that dialectic-as a method parallel but inferior to demonstration-was superseded by the discovery of the scientific method, 2 or that dialectic-as a method of discussing first principles and of eliciting assent during debate-is at best a propadeutic to philosophic inquiry. 3 These assessments are a consequence of the view that, what-1 J. D. G. Evans, Aristotle's Concept of Dialectic (Cambridge, 1977); G. E. L. Owen, ed., Aristotle on Dialectic: The Topics (Proceedings of the Third Symposium Aristotelicum) (Oxford, 1968); J. Barnes, M. Schofield, and R. Sorabji, eds., Articles on Aristotle (London, 1975). See the works mentioned in notes 2 to 9, below. 2 F. Solmsen, "Dialectic without the Forms," in Aristotle on Dialectic (above, note 1), 55 (dialectic's "extraordinary and almost appalling loss of status"), and P. Huby, "The Date of Aristotle's Topics and its Treatment of the Theory of Ideas," Classical Quarterly, N.S. 12 (1962), 72, note 1,76,79-80. This view of dialectic's lossof status is usually connected to the belief that the Topics is one of Aristotle's early works (see Huby, "Date of Aristotle's Topics," and W. D. Ross, Aristotle (London, 1923), 56-57, 59). Solmsen, however, maintains that Aristotle had "a very clear idea" of the difference between dialectical and demonstrative arguments when he wrote the Topics, even though the Posterior Analytics was probably written later ("Dialectic without the Forms," 55). 3 J. Brunschwig, Aristote: Topiques (Livres I-IV) (Paris, 1967), xi-xii; Solmsen, "Dialectic without the Forms," 53-54.

We introduce a semantics of Logic Programming based on classical Game Theory, which is proven to be sound and complete w.r.t. traditional semantics like the minimum Herbrand model and the s-semantics. This AND compositional game semantics allows a very simple characterization of the solution set of a logic program in term of approximations of the value of the game associated to it, which can also be used to capture in a very simple way the traditional "negation as failure" extensions. This novel approach to semantics opens the way to a better understanding of the mechanisms at work in parallel implementations of logic programs, and is of great pedagogical value.

In this paper we recast the formalism of argumentation formalism known as DeLP (Defeasible Logic Programming) in game-theoretic terms. By considering a game between a Proponent and an Opponent, in which they present arguments for and against each literal we obtain a bigger gamut of truth values for those literals and their negations as they are defended and attacked. An important role in the determination of warranted literals is assigned to a defeating relation among arguments. We consider first an unrestricted version in which these games may be infinite and then we analyze the underlying assumptions commonly used to make them finite. Under these restrictions the games are always determined-one of the players has a winning strategy. We show how varying the defeating relation may alter the set of truth values reachable under this formalism. We also show how alternative characterizations of the defeating relation may lead to different assignations of truth values to the literals in a DeLP program.

We present a mathematical model which is the most abstract allowing (i) a fully compositional semantics for timed CSP and (ii) a natural abstraction map into the standard failures/divergences model of untimed CSP. We discuss the construction and properties of this model and ways in which it can be used to give semantics to CSP reflecting several implementation strategies.

Game semantics is a powerful method of semantic analysis for programming languages. It gives mathematically accurate models ("fully abstract") for a wide variety of programming languages. Game semantic models are combinatorial characterisations of all possible interactions between a term and its syntactic context. Because such interactions can be concretely represented as sets of sequences, it is possible to ask whether they can be learned from examples. Concretely, we are using long short-term memory neural nets (LSTM), a technique which proved effective in learning natural languages for automatic translation and text synthesis, to learn game-semantic models of sequential and concurrent versions of Idealised Algol (IA), which are algorithmically complex yet can be concisely described. We will measure how accurate the learned models are as a function of the degree of the term and the number of free variables involved. Finally, we will show how to use the learned model to perform latent semantic analysis between concurrent and sequential Idealised Algol.

Information stored in logs of a computer system is of crucial importance to gather forensic evidence of investigated actions or attacks against the system. Analysis of this information should be rigorous and credible, hence it lends itself to formal methods. We propose a model checking approach to the formalization of the forensic analysis of logs. The set of logs of a certain system is modeled as a tree whose labels are events extracted from the logs. In order to provide a structure to these events, we express each event as a term of a term algebra. The signature of the algebra is carefully chosen to include all relevant information necessary to conduct the analysis. Properties of the model are expressed as formulas of a logic having dynamic, linear, temporal, and modal characteristics. Moreover, we provide a tableau-based proof system for this logic upon which a model checking algorithm can be developed. In order to illustrate the proposed approach, the Windows auditing system is studied. The properties that we capture in our logic include invariant properties of a system, forensic hypotheses, and generic or specific attack signatures. Moreover, we discuss the admissibility of forensics hypotheses and the underlying verification issues.

This paper investigates different readings of plural and reciprocal sentences and how they can be derived from syntactic surface structures in a systematic way. The main thesis is that these readings result from different ways of inserting logical operators at the level of Logical Form. The basic operator considered here is a cumulative mapping from predicates that apply to singularities onto the corresponding predicates that apply to pluralities. Given a theory which allows for free insertion of such operators, it can then be shown that the lexical semantics of the reciprocal expressions each other/one another consists of exactly two components, namely an anaphoric variable and a non-identity statement. This receives further support from the observation that it is exactly these two components that can be focussed by only; all that remains to be done is to correctly manipulate these components at the level of LF.

Let k be a field of positive characteristic p. One considers some categories, whose objects are given classes of finite pgroups, and morphisms are given classes of k-virtual bisets, i.e., linear combinations of bisets with coefficients in k. The category of k-linear functors from such a category to the category of k-vector spaces is abelian, and one can try to classify and describe its simple objects, or its projective objects. By specific subfunctors of the Burnside functor, which have a unique simple quotient S Q,k , one will get some estimates on the k-dimension of the evaluations of these simple functors. These evaluations are equalities for abelian p-groups, and for such groups P the result is even stronger, since it provides some explicit k-bases for the evaluations S Q,k (P).

We introduce and discuss a notion of strictly arithmetical completeness r&ted 10 relative compl&zness of Cook (1978) and arithmetical completeness of Hare1 (1978). We present a powerful technique of obtaining strictly arithmetical axiomatizations of logics of programs. Given a modeltheoretic semantics of' a logic and a set of formulae defining (in a metalanguagei its nonclassical connectives, we automatically derive strictly arithmetically complete and sound proof systems for this logic. As examples of applicdion of the technique we obtain new aGomatiz.ations ofalgorithmic logic, (concurrent) dynamic logic and :empozd logic.