Situational aspects of action are discussed. The presented approach emphasizes the role of situational contexts in which actions are performed. These contexts influence the course of an action; they are determined not only by the current state of the system but also shaped by other factors as time, the previously undertaken actions and their succession, the agents of actions and so on. The distinction between states and situations is explored from the perspective of action systems. The notion of a situational (...) action system is introduced and its theory is expounded. Numerous examples illustrate the reach of the theory. (shrink)

Abramsky, S., Domain theory in logical form, Annals of Pure and Applied Logic 51 1–77. The mathematical framework of Stone duality is used to synthesise a number of hitherto separate developments in theoretical computer science.• Domain theory, the mathematical theory of computation introduced by Scott as a foundation for detonational semantics• The theory of concurrency and systems behaviour developed by Milner, Hennesy based on operational semantics.• Logics of programsStone duality provides a junction between semantics and logics . Moreover, the underlying (...) logic is geometric, which can be computationally interpreted as the logic of observable properties—i.e., properties which can be determined to hold of a process on the basis of a finite amount of information about its execution.These ideas lead to the following programme. A metalanguage is introduced, comprising• types = universes of discourse for various computational situations;• terms = PROGRAMS = syntactic intensions for models or points. A standard denotational interpretation of the metalanguage is given, assigning domains to types and domain elements to terms. The metalanguage is also given a logical interpretation, in which types are interpreted as propositional theories and terms are interpreted via a program logic, which axiomatises the properties they satisfy. The two interpretations are related by showing that they are Stone duals of each other. Hence, semantics and logic are guaranteed to be in harmony with each other, and in fact each determines the other up to isomorphism. This opens the way to a whole range of applications. Given a denotational description of a computational situation in our metalanguage, we can turn the handle to obtain a logic for that situation. (shrink)

This paper provides a formal analysis on the solutions of the frame problem by using dynamic logic. We encode Pednault's syntax-based solution, Baker's state-minimization policy, and Gelfond & Lifchitz's Action Language A in the propositional dynamic logic (PDL). The formal relationships among these solutions are given. The results of the paper show that dynamic logic, as one of the formalisms for reasoning about dynamic domains, can be used as a formal tool for comparing, analyzing and unifying logics of action.

In the artificial intelligence literature a promising approach to counterfactual reasoning is to interpret counterfactual conditionals based on causal models. Different logics of such causal counterfactuals have been developed with respect to different classes of causal models. In this paper I characterize the class of causal models that are Lewisian in the sense that they validate the principles in Lewis’s well-known logic of counterfactuals. I then develop a system sound and complete with respect to this class. The resulting logic is (...) the weakest logic of causal counterfactuals that respects Lewis’s principles, sits in between the logic developed by Galles and Pearl and the logic developed by Halpern, and stands to Galles and Pearl’s logic in the same fashion as Lewis’s stands to Stalnaker’s. (shrink)

This is the first paper on constructive concurrent dynamic logic . For the first time, either for concurrent or sequential dynamic logic, we give a satisfactory treatment of what statements are forced to be true by partial information about the underlying computer. Dynamic logic was developed by Pratt [V. Pratt, Semantical considerations on Floyd–Hoare logic, in: 17th Annual IEEE Symp. on Found. Comp. Sci., New York, 1976, pp. 109–121, V. Pratt, Applications of modal logic to programming, Studia Logica 39 257–274] (...) for nondeterministic sequential programs, and by Peleg [D. Peleg, Concurrent dynamic logic, Journal of the Association for Computing Machinery 34 , D. Peleg, Communication in concurrent dynamic logic, Journal of Computer and System Sciences 35 ] for concurrent programs, for the purpose of proving properties of programs such as correctness. Here we define what it means for a dynamic logic formula to be forced to be true knowing only partial information about the results of assignments and tests. This informal CCDL semantics is formalized by intuitionistic Kripke frames modeling this partial information, and each such frame is interpreted as an idealized concurrent machine . In CCDL, proofs and deductions are ω-height, ω-branching, well-founded labeled subtrees of ωω. These are a generalization of the signed tableaux of Nerode [A. Nerode, Some lectures in modal logic, Technical Report, M.S.I. Cornell University, 1989, CIME Logic and Computer Science Montecatini Volume, Springer-Verlag Lecture Notes, 1990, A. Nerode, Some lectures in intuitionistic logic, Technical Report, M.S.I. Cornell University, 1988, Marktoberdorf Logic and Computation NATO Summer School Volume, NATO Science Series, 1990 ] stemming from the prefix tableaux of Fitting [M.C. Fitting, Proof Methods for Modal and Intuitionistic Logic, Reidel, 1983]. We demonstrate the correctness of our tableau proofs, define consistency properties, prove that consistency properties yield models, construct systematic tableaux, prove that systematic tableaux yield a consistency property, and conclude that CCDL is complete. This infinitary semantics and proof procedure will be the primary guide for defining, in a sequel, the correct finitary CCDL based on induction principles. FCCDL is suitable for implementation in constructive logic software systems such as Constable’s NUPRL or Huet-Coquand’s CONSTRUCTIONS. Our goal is to develop a constructive logic programming tool for specification and modular verification of programs in any imperative concurrent language, and for the extraction of concurrent programs from constructive proofs. Subsequent papers will introduce analogous logics for declarative and functional concurrent languages. (shrink)

ABSTRACT Propositional dynamic logic with converse and test, is enriched with complement, intersection and relational operations of weakest prespecification and weakest postspecification. Relational deduction system for the logic is given based on its interpretation in the relational calculus. Relational interpretation of the operators ?repeat? and ?loop? is given.

Many powerful logics exist today for reasoning about multi-agent systems, but in most of these it is hard to reason about an infinite or indeterminate number of agents. Also the naming schemes used in the logics often lack expressiveness to name agents in an intuitive way.To obtain a more expressive language for multi-agent reasoning and a better naming scheme for agents, we introduce a family of logics called term-modal logics. A main feature of our logics is the use of modal (...) operators indexed by the terms of the logics. Thus, one can quantify over variables occurring in modal operators. In term-modal logics agents can be represented by terms, and knowledge of agents is expressed with formulas within the scope of modal operators. (shrink)

This volume presents mathematical game theory as an interface between logic and philosophy.

It is well established by now that computer science has a number of concerns in common with natural language understanding. Common themes show up in particular with algorithmic aspects of text processing. This chapter gives an overview of border crossings from NLP to CS and back. Starting out from syntactic analysis, we trace our route via a philosophical puzzle about meaning, Hoare correctness rules for dynamic semantics, error state analysis of presupposition, equational reasoning about state change, programming with frameworks originally (...) devised for natural language semantics, and the logic of incremental processing. In many cases methods and perspectives developed on one side of the border proved quite useful on the other side, although usually it becomes clear after a while that tools have to be redesigned to fit. The chapter ends with a sketch of the emerging contours of a ‘proper treatment of context in natural language’ that is more than just an application of a logic designed for program analysis. (shrink)

This thesis studies Judea Pearl’s logic of counterfactuals derived from the causal modeling framework, in comparison to the influential Stanlnaker-Lewis counterfactual logics. My study focuses on a characteristic principle in Pearl’s logic, named reversibility. The principle, as Pearl pointed out, goes beyond Lewis’s logic. Indeed, it also goes beyond the stronger logic of Stanlnaker, which is more analogous to Pearl’s logic. The first result of this thesis is an extension of Stanlnaker’s logic incorporating reversibility. It will be observed that the (...) translation of reversibility from Pearl’s language to the standard language for conditional logic deserves some attention. In particular, a straightforward translation following Pearl’s suggestion would render reversibility incompatible with Stanlnaker’s logic. A new translation of reversibility will be proposed, and an extension of Stanlnaker’s logic with the inclusion of the translated reversibility will be investigated. More importantly, it will be shown that the extended Stanlnaker’s logic is sound and complete with respect to a modified Stanlnaker’s semantics. The extension of Stanlnaker’s logic has an interesting implication. Zhang, Lam, and de Clercq have shown that special case of reversibility, despite its name, actually states an important kind of irreversibility: counterfactual dependence between distinct events is irreversible. In other words, reversibility entails that there is no cycle of counterfactual dependence altogether generalizations of reversibility. However, as shown in Zhang et al., Pearls’ logic does not rule out cycles of counterfactual dependence altogether. It in fact allows cycles that involve three or more distinct events. This is peculiar because the status of cyclic counterfactual dependence seems no more metaphysically secure than that of mutual counterfactual dependence. This consideration leads to an exploration of logics that rule out all cycles of counterfactual dependence. A surprising result is that the extension of Stanlnaker’s logic is precisely a logic of this sort. (shrink)

This dissertation addresses a variety of foundational issues pertaining to the notion of algorithm employed in mathematics and computer science. In these settings, an algorithm is taken to be an effective mathematical procedure for solving a previously stated mathematical problem. Procedures of this sort comprise the notional subject matter of the subfield of computer science known as algorithmic analysis. In this context, algorithms are referred to via proper names of which computational properties are directly predicated )). Moreover, many formal results (...) are traditionally stated by explicitly quantifying over algorithms. These observations motivate the view that algorithms are themselves abstract mathematical objects -- a view I refer to as algorithmic realism. The status of this view is clearly related to that of Church's Thesis -- i.e. the claim that a function is computable by an algorithm just in case it is partial recursive. But whereas Church's Thesis is widely accepted on the basis of several well-known mathematical analyses of algorithmic computability, there is presently no consensus on how we can uniformly identify individual algorithms with mathematical objects. In the first chapter of this work, I attempt to illustrate the theoretical significance of algorithmic realism. I suggest that this view is not only of foundational significance to computer science, but also worth highlighting due to the role algorithms play in the fixation of mathematical knowledge and their relationship to intensional entities such as propositions and properties. Chapter Two presents a formal framework for reducing computational discourse to mathematical discourse modeled on contemporary discussion of mathematical nominalism. Chapter Three is centered on a case study intended to illustrate the technical exigencies involved with defending algorithmic realism. Chapter Four explores various ways in which algorithms might be identified with models of computation. And finally, Chapter Five argues that no such identification can uniformly satisfy all statements of algorithmic identity and non-identity affirmed by computational practice. I suggest that the technical crux of algorithmic realism lies in the necessity of reducing recursive specifications of algorithms to iterative models of computation in a manner which preserves algorithmic identity. (shrink)