ATL and Strategy Logic (SL) are important languages for representation and reasoning about strategic abilities of coalitions in multi-agent systems. In analyzing strategies of agents in multi-agent systems, an important concept to consider is rationality. Strategy Logic can express rationality concepts such as Nash Equilibrium (NE). Recently, there has been work on logics for joint abilities incorporating rationality concepts based on iterated elimination of dominated strategies (IEDS). Each of NE and IEDS has its strengths and limitations. However, when the payoff is binary, e.g., whether a goal is satisfied, IEDS has more distinguishing power than NE. In this work, we propose Strategy Logic with IEDS (SL_{IEDS}), an extension of Strategy Logic with an IEDS operator, where we can reason about rational strategies that survive IEDS. We prove that SL_{IEDS} is strictly more expressive than SL. Finally, we prove that model checking memoryless SL_{IEDS} is EXPTIME-complete.

Generalized planning is concerned with how to find a single plan to solve multiple similar planning instances. Abstractions are widely used for solving generalized planning, and QNP (qualitative numeric planning) is a popular abstract model. Recently, Cui et al. showed that a plan solves a sound and complete abstraction of a generalized planning problem if and only if the refined plan solves the original problem. However, existing work on automatic abstraction for generalized planning can hardly guarantee soundness let alone completeness. In this paper, we propose an automatic sound and complete abstraction method for generalized planning with baggable types. We use a variant of QNP, called bounded QNP (BQNP), where integer variables are increased or decreased by only one. Since BQNP is undecidable, we propose and implement a sound but incomplete solver for BQNP. We present an automatic method to abstract a BQNP problem from a classical planning instance with baggable types. The basic idea for abstraction is to introduce a counter for each bag of indistinguishable tuples of objects. We define a class of domains called proper baggable domains, and show that for such domains, the BQNP problem got by our automatic method is a sound and complete abstraction for a generalized planning problem whose instances share the same bags with the given instance but the sizes of the bags might be different. Thus, the refined plan of a solution to the BQNP problem is a solution to the generalized planning problem. Finally, we implement our abstraction method and experiments on a number of domains demonstrate the promise of our approach.

Coordination and joint ability are important topics in representation and reasoning about multi-agent systems. The modal logic JAADL proposed by Liu et al. extends ATL with joint abilities, which enables reasoning about whether a coalition of agents can coordinate and achieve a goal without communication. However, like ATL, strategic abilities in JAADL are defined in terms of combinatorial strategies, which are functions from histories or states to actions. On the other hand, there has been research on reasoning about natural strategic abilities, where a natural strategy is formalized as a sequence of condition-action pairs, making it more human-friendly than combinatorial strategy. In this work, we propose SJAADL, a variation of JAADL where strategic abilities are defined in terms of structured strategies represented with LDL (linear dynamic logic) formulas, with bounded complexity. We use nondeterministic strategies since they are more expressive, natural and succinct than determinstic ones. We present syntax and semantics of SJAADL. We show that model checking SJAADL can be done in time quasi-polynomial with the model size, exponential with the formula size, and with the complexity bound of structured strategies, exponential in the memoryless case and double exponential in the memoryful case. Finally, we introduce the problem of synthesizing norms to achieve joint abilities, and give two algorithms for it.

Non-monotonic reasoning (NMR) refers to the fact that conclusions may be invalidated by new information.It is widely used in daily life and legal reasoning.An NMR task usually has multiple extensions, which are sets of plausible conclusions.There are two reasoning modesskeptical and credulous reasoning, depending on whether to believe facts in all extensions or any one extension.Despite some preliminary work exploring the NMR abilities of LLMs, the multi-extension NMR capabilities of LLMs remain underexplored.In this paper, we synthesize a multi-extension NMR dataset Multi-LogicNMR, and construct two variants of the dataset with more extensions or text diversity.We propose a neural-symbolic framework Mul-tiLogicNMRer for multi-extension NMR.Experimental evaluation with the datasets shows that LLMs still face significant challenges in NMR abilities, and reveal the effectiveness of our neural-symbolic framework, with an average accuracy gain of about 15% compared to prompt-based methods, and even outperforming some fine-tuning methods.All code and data are publicly available 1 .

Qualitative Numerical Planning (QNP) extends classical planning with numerical variables that can be changed by arbitrary amounts. FOND+ extends Fully Observable Non-Deterministic (FOND) planning by introducing explicit fairness assumptions, resulting in a more expressive model that can also capture QNP as a special case. However, existing QNP and FOND+ solvers still face significant scalability challenges. To address this, we propose a novel framework for solving QNP and FOND+ by generating strong cyclic solutions of the associated FOND problem, testing their validity, and forbidding non-solutions in conducting further searches. For this, we propose a procedure called SIEVE*, which generalizes the QNP termination testing algorithm SIEVE to determine whether a strong cyclic solution is a FOND+ solution. Additionally, we propose several optimization techniques to further improve the performance of our basic framework. We implemented our approach based on the advanced FOND solver PRP; experimental results show that our solver shows superior scalability over the existing QNP and FOND+ solvers.

Reasoning about actions and change (RAC) is essential to understand and interact with the ever-changing environment.Previous AI research has shown the importance of fundamental and indispensable knowledge of actions, i.e., preconditions and effects.However, traditional methods rely on logical formalization which hinders practical applications.With recent transformer-based language models (LMs), reasoning over text is desirable and seemingly feasible, leading to the question of whether LMs can effectively and efficiently learn to solve RAC problems.We propose four essential RAC tasks as a comprehensive textual benchmark and generate problems in a way that minimizes the influence of other linguistic requirements (e.g., grounding) to focus on RAC.The resulting benchmark, TRAC, encompassing problems of various complexities, facilitates a more granular evaluation of LMs, precisely targeting the structural generalization ability much needed for RAC.Experiments with three high-performing transformers indicate that additional efforts are needed to tackle challenges raised by TRAC.

Belief change studies how an agent modifies her beliefs on receiving new information. However, so far most research on belief change works on beliefs represented in propositional logic. There have been many works on integrating belief revision with reasoning about actions, and some works extending belief change from propositional logic to epistemic logics. In this paper, we study revision on beliefs of a third person represented with the multi-agent KD45 logic. Our formal technique is analogous to that of distance-based belief revision in propositional logic: to revise a KB by a formula, select from models of the formula those that are closest to models of the KB. To this end, a challenge is that in modal logics, a formula may have infinitely many Kripke models. To tackle this, we propose a variant of Moss’ canonical formulas called alternating canonical formulas, treat them as models for formulas, and define a notion of distance between them, based on the Hausdorff distance between two sets. We show that our revision satisfies all of the AGM postulates. To give syntactic characterizations of our revision, we make use of a normal form for KD45n called alternating cover disjunctive formulas (ACDFs). We give syntactic characterizations firstly on fragments of ACDFs called proper ACDFs and alternating cover conjunctive formulas (ACCFs), and finally on the whole ACDFs.

Coordination and joint ability are important problems in representation and reasoning about multi-agent systems. Ghaderi et al. presented a formalization of joint ability of coalitions in the expressive first-order language of the situation calculus. Essentially, a coalition has joint ability to achieve a goal if after iterated elimination of dominated strategies, any remaining joint strategy achieves the goal. Based on their work, Liu et al. proposed JAADL, a modal logic for joint abilities under strategy commitments. In this paper, we propose EJAADL, an epistemic extension of JAADL, for imperfect information games where agents may have incomplete knowledge or even false beliefs about the world. Like Ghaderi et al.’s work, elimination of dominated strategies is now based on beliefs about the world, rather than facts about the world as in JAADL. Strategies are required to be uniform, i.e., they select the same action in all accessible histories. We illustrate EJAADL with examples, analyze its properties, and show that model checking memoryless EJAADL is in EXPTIME. Moreover, we consider the fragment of EJAADL without the iterated elimination operator, and show that model-checking the memoryless version of this fragment can be done in PSPACE.

Generalized planning (GP) studies the computation of general solutions for a set of planning problems. Computing general solutions with correctness guarantee has long been a key issue in GP. Abstractions are widely used to solve GP problems. For example, a popular abstraction model for GP is qualitative numeric planning (QNP), which extends classical planning with non-negative real variables that can be increased or decreased by some arbitrary amount. The refinement of correct solutions of sound abstractions are solutions with correctness guarantees for GP problems. More recent literature proposed a uniform abstraction framework for GP and gave model-theoretic definitions of sound and complete abstractions for GP problems. In this paper, based on the previous work, we explore automatic verification of sound abstractions for GP. Firstly, we present a proof-theoretic characterization for sound abstractions. Secondly, based on the characterization, we give a sufficient condition for sound abstractions with deterministic actions. Then we study how to verify the sufficient condition when the abstraction models are bounded QNPs where integer variables can be incremented or decremented by one. To this end, we develop methods to handle counting and transitive closure, which are often used to define numerical variables. Finally, we implement a sound bounded QNP abstraction verification system and report experimental results on several domains.

Table fact verification aims to check the correctness of textual statements based on given semi-structured data.Most existing methods are devoted to better comprehending logical operations and tables, but they hardly study generating latent programs from statements, with which we can not only retrieve evidences efficiently but also explain reasons behind verifications naturally.However, it is challenging to get correct programs with existing weakly supervised semantic parsers due to the huge search space with lots of spurious programs.In this paper, we address the challenge by leveraging both lexical features and structure features for program generation.Through analyzing the connection between the program tree and the dependency tree, we define a unified concept, operation-oriented tree, to mine structure features, and introduce Structure-Aware Semantic Parsing to integrate structure features into program generation.Moreover, we design a refined objective function with lexical features and violation punishments to further avoid spurious programs.Experimental results show that our proposed method generates programs more accurately than existing semantic parsers, and achieves comparable performance to the SOTA on the large-scale benchmark TABFACT.

Qualitative numeric planning (QNP) is classical planning extended with non-negative real variables that can be increased or decreased by some arbitrary amount. Existing approaches for solving QNP problems are exclusively based on compilation to fully observable nondeterministic planning (FOND) problems or FOND+ problems, i.e., FOND problems with explicit fairness assumptions. However, the FOND-compilation approaches suffer from some limitations, such as difficulties to generate all strong cyclic solutions for FOND problems or introducing a great many extra variables and actions. In this paper, we propose a simpler characterization of QNP solutions and a new approach to solve QNP problems based on directly searching for a solution, which is a closed and terminating subgraph that contains a goal node, in the AND/OR graphs induced by QNP problems. Moreover, we introduce a pruning strategy based on termination tests on subgraphs. We implemented a native solver DSET based on the proposed approach and compared the performance of it with that of the two compilation-based approaches. Experimental results show that DSET is faster than the FOND-compilation approach by one order of magnitude, and comparable with the FOND+-compilation approach.

The recent success of neural language models (NLMs) on the Winograd Schema Challenge has called for further investigation of the commonsense reasoning ability of these models.Previous diagnostic datasets rely on crowd-sourcing which fails to provide coherent commonsense crucial for solving WSC problems.To better evaluate NLMs, we propose a logic-based framework that focuses on highquality commonsense knowledge.Specifically, we identify and collect formal knowledge formulas verified by theorem provers and translate such formulas into natural language sentences.Based on these true knowledge sentences, adversarial false ones are generated.We propose a new dataset named WINOLOGIC with these sentences.Given a problem in WINOLOGIC, NLMs need to decide whether the plausible knowledge sentences could correctly solve the corresponding WSC problems in a zero-shot setting.We also ask human annotators to validate WINOLOGIC to ensure it is humanagreeable.Experiments show that NLMs still struggle to comprehend commonsense knowledge as humans do, indicating that their reasoning ability could have been overestimated.

Generalized planning aims at finding a general solution for a set of similar planning problems. Abstractions are widely used to solve such problems. However, the connections among these abstraction works remain vague. Thus, to facilitate a deep understanding and further exploration of abstraction approaches for generalized planning, it is important to develop a uniform abstraction framework for generalized planning. Recently, Banihashemi et al. proposed an agent abstraction framework based on the situation calculus. However, expressiveness of such an abstraction framework is limited. In this paper, by extending their abstraction framework, we propose a uniform abstraction framework for generalized planning. We formalize a generalized planning problem as a triple of a basic action theory, a trajectory constraint, and a goal. Then we define the concepts of sound abstractions of a generalized planning problem. We show that solutions to a generalized planning problem are nicely related to those of its sound abstractions. We also define and analyze the dual notion of complete abstractions. Finally, we review some important abstraction works for generalized planning and show that they can be formalized in our framework.

Representation and reasoning about strategic abilities has been an active research area in AI and multi-agent systems. Many variations and extensions of alternating-time temporal logic ATL have been proposed. However, most of the logical frameworks ignore the issue of coordination within a coalition, and are unable to specify the internal structure of strategies. In this paper, we propose JAADL, a modal logic for joint abilities under strategy commitments, which is an extension of ATL. Firstly, we introduce an operator of elimination of (strictly) dominated strategies, with which we can represent joint abilities of coalitions. Secondly, our logic is based on linear dynamic logic (LDL), an extension of linear temporal logic (LTL), so that we can use regular expressions to represent commitments to structured strategies. We analyze valid formulas in JAADL, give sufficient/necessary conditions for joint abilities, and show that model checking memoryless JAADL is in EXPTIME.

Strategy representation and reasoning has received much attention over the past years. In this paper, we consider the representation of general strategies that solve a class of (possibly infinitely many) games with similar structures, and their automatic verification, which is an undecidable problem. We propose to represent a general strategy by an FSA (Finite State Automaton) with edges labelled by restricted Golog programs. We formalize the semantics of FSA strategies in the situation calculus. Then we propose an incomplete method for verifying whether an FSA strategy is a winning strategy by counterexample-guided local search for appropriate invariants. We implemented our method and did experiments on combinatorial game and also single-agent domains. Experimental results showed that our system can successfully verify most of them within a reasonable amount of time.

In the past decade, multi-agent epistemic planning has received much attention from both dynamic logic and planning communities. Common knowledge is an essential part of multi-agent modal logics, and plays an important role in coordination and interaction of multiple agents. However, existing implementations of multi-agent epistemic planning provide very limited support for common knowledge, basically static propositional common knowledge. Our work aims to extend an existing multi-agent epistemic planning framework based on higher-order belief change with the capability to deal with common knowledge. We propose a novel normal form for multi-agent KD45 logic with common knowledge. We propose satisfiability solving, revision and update algorithms for this normal form. Based on our algorithms, we implemented a multi-agent epistemic planner with common knowledge called MEPC. Our planner successfully generated solutions for several domains that demonstrate the typical usage of common knowledge.

In recent years, multi-agent epistemic planning has received attention from both dynamic logic and planning communities. Existing implementations of multi-agent epistemic planning are based on compilation into classical planning and suffer from various limitations, such as generating only linear plans, restriction to public actions, and incapability to handle disjunctive beliefs. In this paper, we propose a general representation language for multi-agent epistemic planning where the initial KB and the goal, the preconditions and effects of actions can be arbitrary multi-agent epistemic formulas, and the solution is an action tree branching on sensing results.To support efficient reasoning in the multi-agent KD45 logic, we make use of a normal form called alternative cover disjunctive formula (ACDF). We propose basic revision and update algorithms for ACDF formulas. We also handle static propositional common knowledge, which we call constraints. Based on our reasoning, revision and update algorithms, adapting the PrAO algorithm for contingent planning from the literature, we implemented a multi-agent epistemic planner called MAEP. Our experimental results show the viability of our approach.

Golog is a logic programming language for high-level agent control. In a recent paper, we proposed a sound but incomplete method for automatic verification of partial correctness of Golog programs where we give a number of heuristic methods to strengthen given formulas in order to discover loop invariants. However, our method does not work on arithmetic domains. On the other hand, the method of predicate abstraction is widely used in the software engineering community for model checking and partial correctness verification of programs. Intuitively, the predicate abstraction task is to find a formula consisting of a given set of predicates to approximate a given first-order formula. In this paper, we propose a method for automatic verification of partial correctness of Golog programs which use predicate abstraction as a uniform method to strengthen given formulas. We implement a system based on the proposed method, conduct experiments on arithmetical domains and examples from the paper by Li and Liu. Also, we apply our method to the verification of winning strategies for combinatorial games.

Strategy representation and reasoning has been one of the most active research areas in AI and multi-agent systems. Representative strategic logics are ATL and the more expressive Strategy Logic SL which reasons about strategies explicitly. In this paper, by a simple extension of the situation calculus with a strategy sort, we develop a general framework for strategy representation and reasoning for complete information games. This framework can be used to compactly represent both concurrent and turn-based possibly infinite game structures, specify the internal structure of strategies, reason about strategies explicitly, and reason about strategic abilities of coalitions under commitments to strategy specifications. We show that our framework is strictly more expressive than SL, and inspired by the work of De Giacomo et al. on bounded action theories, give a decidable fragment of our framework.

Belief change is an important research topic in AI. It becomes more perplexing in multi-agent settings, since the action of an agent may be partially observable to other agents. In this paper, we present a general approach to reasoning about actions and belief change in multi-agent settings. Our approach is based on a multi-agent extension to the situation calculus, augmented by a plausibility relation over situations and another one over actions, which is used to represent agents' different perspectives on actions. When an action is performed, we update the agents' plausibility order on situations by giving priority to the plausibility order on actions, in line with the AGM approach of giving priority to new information. We show that our notion of belief satisfies KD45 properties. As to the special case of belief change of a single agent, we show that our framework satisfies most of the classical AGM, KM, and DP postulates. We also present properties concerning the change of common knowledge and belief of a group of agents.

While founded on the situation calculus, current implementations of Golog are mainly based on the closed-world assumption or its dynamic versions or the domain closure assumption. Also, they are almost exclusively based on regression. In this paper, we propose a first-order interpreter for knowledge-based Golog with sensing based on exact progression and limited reasoning. We assume infinitely many unique names and handle first-order disjunctive information in the form of the so-called proper+ KBs. Our implementation is based on the progression and limited reasoning algorithms for proper+ KBs proposed by Liu, Lakemeyer and Levesque. To improve efficiency, we implement the two algorithms by grounding via a trick based on the unique name assumption. The interpreter is online but the programmer can use two operators to specify offline execution for parts of programs. The search operator returns a conditional plan, while the planning operator is used when local closed-world information is available and calls a modern planner to generate a sequence of actions.

In a previous paper, Liu argued for the importance of establishing a precise theoretical foundation for program debugging from first principles. In this paper, we present a first step towards a theoretical exploration of program debugging algorithms. The starting point of our work is the recent debugging approach based on predicate switching. The idea is to switch the outcome of an instance of a predicate to bring the program execution to a successful completion and then identify the fault by examining the switched predicate. However, no theoretical analysis of the approach is available. In this paper, we generalize the above idea, and propose the bounded debugging via multiple predicate switching (BMPS) algorithm, which locates faults through switching the outcomes of instances of multiple predicates to get a successful execution where each loop is executed for a bounded number of times. Clearly, BMPS can be implemented by resorting to a SAT solver. We focus attention on RHS faults, that is, faults that occur in the control predicates and right-hand-sides of assignment statements. We prove that for conditional programs, BMPS is quasi-complete for RHS faults in the sense that some part of any true diagnosis will be returned by BMPS; and for iterative programs, when the bound is sufficiently large, BMPS is also quasi-complete for RHS faults. Initial experimentation with debugging small C programs showed that BMPS can quickly and effectively locate the faults.

Levesque proposed a generalization of a database called a proper knowledge base (KB), which is equivalent to a possibly infinite consistent set of ground literals. In contrast to databases, proper KBs do not make the closed-world assumption and hence the entailment problem becomes undecidable. Levesque then proposed a limited but efficient inference method V for proper KBs, which is sound and, when the query is in a certain normal form, also logically complete. He conjectured that for every first-order query there is an equivalent one in normal form. In this note, we show that this conjecture is false. In fact, we show that any class of formulas for which V is complete must be strictly less expressive than full first-order logic. Moreover, in the propositional case it is very unlikely that a formula always has a polynomial-size normal form.

Blocks World (BW) has been one of the most popular model domains in AI history. However, there has not been serious work on axiomatizing the state constraints of BW and giving justification for its soundness and completeness. In this paper, we model a state of BW by a finite collection of finite chains, and call the theory of all these structures BW theory. We present seven simple axioms and prove that their consequences are precisely BW theory, using Ehrenfeucht-Fraïssé games. We give a simple decision procedure for the theory which can be implemented in exponential space, and prove that every decision procedure (even if nondeterministic) for the theory must take at least exponential time. We also give a characterization of all nonstandard models for the theory. Finally, we present an expansion of BW theory and show that it admits elimination of quantifiers. As a result, we are able to characterize all definable predicates in BW theory, and give simple examples of undefinable predicates.