Natasha Alechina

Categorical and Kripke Semantics for Constructive S4 Modal Logic

We consider two systems of constructive modal logic which are computationally motivated. Their modalities admit several computational interpretations and are used to capture intensional features such as notions of computation, constraints, concurrency, etc. Both systems have so far been studied mainly from type-theoretic and category-theoretic perspectives, but Kripke models for similar systems were studied independently. Here we bring these threads together and prove duality results which show how to relate Kripke models to algebraic models and these in turn to the appropriate categorical models for these logics.

A modal perspective on path constraints

Several classes of path constraints for semistructured data are analysed and a number of decidability and complexity results proved for such constraints. While some of these decidability results were known before, it is believed that the improved complexity bounds are new. Proofs are based on techniques from modal logic and automata theory. This modal logic perspective sheds additional light on the reasons for previously known decidability and complexity results.

A Complete and Decidable Logic for Resource-Bounded Agents

We propose a context-logic style formalism, Timed Reasoning Logics (TRL), to describe resource-bounded reasoners who take time to derive consequences of their knowledge. The semantics of TRL is grounded in the agentýs computation, allowing an unambiguous ascription of the set of formulas which the agent actually knows at time t. We show that TRL can capture various rule application and conflict resolution strategies that a rule-based agent may employ, and analyse two examples in detail: TRL(STEP) which models an all rules at each cycle strategy similar to that assumed in step logic [5], and TRL(CLIPS) which models a single rule at each cycle strategy similar to that employed by the CLIPS [22] rule based system architecture.We prove a general completeness and decidability results for TRL(STEP).

Logic for coalitions with bounded resources1

Recent work on Alternating-Time Temporal Logic and Coalition Logic has allowed the expression of many interesting properties of coalitions and strategies. However there is no natural way of expressing resource requirements in these logics. This paper presents a Resource-Bounded Coalition Logic (RBCL) which has explicit representation of resource bounds in the language, and gives a complete and sound axiomatisation of RBCL.

Reachability logic: an efficient fragment of transitive closure logic

We define reachability logic (RL), a fragment of FO(TC) (with boolean variables) that admits efficient model checking – linear time with a small constant – as a function of the size of the structure being checked. RL is expressive enough so that modal logics PDL and CTL? can be linearly embedded in it. The model checking algorithm is also linear in the size of the formula, but exponential in the number of boolean variables occurring in it. In practice this number is very small. In particular, for CTL and PDL formulas the resulting model checking algorithm remains linear. For CTL? the complexity of model checking — which is PSPACE complete in the worst case — can be read from the face of the translated formula.

The Dynamics of Syntactic Knowledge

The syntactic approach to epistemic logic avoids the logical omniscience problem by taking knowledge as primary rather than as defined in terms of possible worlds. In this study, we combine the syntactic approach with modal logic, using transition systems to model reasoning. We use two syntactic epistemic modalities: ‘knowing at least’ a set of formulae and ‘knowing at most’ a set of formulae. We are particularly interested in models restricting the set of formulae known by an agent at a point in time to be finite. The resulting systems are investigated from the point of view of axiomatization and complexity. We show how these logics can be used to formalise non-omniscient agents who know some inference rules, and study their relationship to other systems of syntactic epistemic logics,

Verifying time, memory and communication bounds in systems of reasoning agents

We present a framework for verifying systems composed of heterogeneous reasoning agents, in which each agent may have differing knowledge and inferential capabilities, and where the resources each agent is prepared to commit to a goal (time, memory and communication bandwidth) are bounded. The framework allows us to investigate, for example, whether a goal can be achieved if a particular agent, perhaps possessing key information or inferential capabilities, is unable (or unwilling) to contribute more than a given portion of its available computational resources or bandwidth to the problem. We present a novel temporal epistemic logic, BMCL-CTL, which allows us to describe a set of reasoning agents with bounds on time, memory and the number of messages they can exchange. The bounds on memory and communication are expressed as axioms in the logic. As an example, we show how to axiomatise a system of agents which reason using resolution and prove that the resulting logic is sound and complete. We then show how to encode a simple system of reasoning agents specified in BMCL-CTL in the description language of the Mocha model checker (Alur et al., Proceedings of the tenth international conference on computer-aided verification (CAV), 1998), and verify that the agents can achieve a goal only if they are prepared to commit certain time, memory and communication resources.

Belief revision for AgentSpeak agents

The AgentSpeak agent-oriented programming language has recently been extended with a number of new features, such as speech-act based communication, internal belief additions, and support for ontological reasoning, which imply a need for belief revision within an AgentSpeak agent. In this paper, we show how a polynomial-time belief-revision algorithm can be incorporated into the Jason AgentSpeak interpreter. To the best of our knowledge, this is the first attempt to include belief revision within an interpreter for a practical agent programming language.

Resource-Bounded belief revision and contraction

Agents need to be able to change their beliefs; in particular, they should be able to contract or remove a certain belief in order to restore consistency to their set of beliefs, and revise their beliefs by incorporating a new belief which may be inconsistent with their previous beliefs. An influential theory of belief change proposed by Alchourron, Gardenfors and Makinson (AGM) [1] describes postulates which rational belief revision and contraction operations should satisfy. The AGM postulates are usually taken as characterising idealised rational reasoners, and the corresponding belief change operations are considered unsuitable for implementable agents due to their high computational cost [2]. The main result of this paper is to show that an efficient (linear time) belief contraction operation nevertheless satisfies all but one of the AGM postulates for contraction. This contraction operation is defined for an implementable rule-based agent which can be seen as a reasoner in a very weak logic; although the agents beliefs are deductively closed with respect to this logic, checking consistency and tracing dependencies between beliefs is not computationally expensive. Finally, we give a non-standard definition of belief revision in terms of contraction for our agent.

Reasoning about agent deliberation

We present a family of sound and complete logics for reasoning about deliberation strategies for SimpleAPL programs. SimpleAPL is a fragment of the agent programming language 3APL designed for the implementation of cognitive agents with beliefs, goals and plans. The logics are variants of PDL, and allow us to prove safety and liveness properties of SimpleAPL agent programs under different deliberation strategies. We show how to axiomatise different deliberation strategies for SimpleAPL programs, and, for each strategy we prove a correspondence between the operational semantics of SimpleAPL and the models of the corresponding logic. We illustrate the utility of our approach with an example in which we show how to verify correctness properties for a simple agent program under different deliberation strategies.