Large Language Models (LLMs) have made significant strides in various intelligent tasks but still struggle with complex action reasoning tasks that require systematic search. To address this limitation, we propose a method that bridges the natural language understanding capabilities of LLMs with the symbolic reasoning strengths of action languages. Our approach, termed LLM+AL, leverages the LLM's strengths in semantic parsing and commonsense knowledge generation alongside the action language's proficiency in automated reasoning based on encoded knowledge. We compare LLM+AL against state-of-the-art LLMs, including ChatGPT-4, Claude 3 Opus, Gemini Ultra 1.0, and o1-preview, using benchmarks for complex reasoning about actions. Our findings indicate that, although all methods exhibit errors, LLM+AL, with relatively minimal human corrections, consistently leads to correct answers, whereas standalone LLMs fail to improve even with human feedback. LLM+AL also contributes to automated generation of action languages.

Causal and temporal reasoning about video dynamics is a challenging problem. While neuro-symbolic models that combine symbolic reasoning with neural-based perception and prediction have shown promise, they exhibit limitations, especially in answering counterfactual questions. This paper introduces a method to enhance a neuro-symbolic model for counterfactual reasoning, leveraging symbolic reasoning about causal relations among events. We define the notion of a causal graph to represent such relations and use Answer Set Programming (ASP), a declarative logic programming method, to find how to coordinate perception and simulation modules. We validate the effectiveness of our approach on two benchmarks, CLEVRER and CRAFT. Our enhancement achieves state-of-the-art performance on the CLEVRER challenge, significantly outperforming existing models. In the case of the CRAFT benchmark, we leverage a large pre-trained language model, such as GPT-3.5 and GPT-4, as a proxy for a dynamics simulator. Our findings show that this method can further improve its performance on counterfactual questions by providing alternative prompts instructed by symbolic causal reasoning.

Large language models (LLMs), such as GPT-3 and GPT-4, have demonstrated exceptional performance in various natural language processing tasks and have shown the ability to solve certain reasoning problems. However, their reasoning capabilities are limited and relatively shallow, despite the application of various prompting techniques. In contrast, formal logic is adept at handling complex reasoning, but translating natural language descriptions into formal logic is a challenging task that non-experts struggle with. This paper proposes a neuro-symbolic method that combines the strengths of large language models and answer set programming. Specifically, we employ an LLM to transform natural language descriptions of logic puzzles into answer set programs. We carefully design prompts for an LLM to convert natural language descriptions into answer set programs in a step by step manner. Surprisingly, with just a few in-context learning examples, LLMs can generate reasonably complex answer set programs. The majority of errors made are relatively simple and can be easily corrected by humans, thus enabling LLMs to effectively assist in the creation of answer set programs.

Injecting discrete logical constraints into neural network learning is one of the main challenges in neuro-symbolic AI. We find that a straight-through-estimator, a method introduced to train binary neural networks, could effectively be applied to incorporate logical constraints into neural network learning. More specifically, we design a systematic way to represent discrete logical constraints as a loss function; minimizing this loss using gradient descent via a straight-through-estimator updates the neural network’s weights in the direction that the binarized outputs satisfy the logical constraints. The experimental results show that by leveraging GPUs and batch training, this method scales significantly better than existing neuro-symbolic methods that require heavy symbolic computation for computing gradients. Also, we demonstrate that our method applies to different types of neural networks, such as MLP, CNN, and GNN, making them learn with no or fewer labeled data by learning directly from known constraints.

We present NeurASP, a simple extension of answer set programs by embracing neural networks. By treating the neural network output as the probability distribution over atomic facts in answer set programs, NeurASP provides a simple and effective way to integrate sub-symbolic and symbolic computation. We demonstrate how NeurASP can make use of a pre-trained neural network in symbolic computation and how it can improve the neural network's perception result by applying symbolic reasoning in answer set programming. Also, NeurASP can make use of ASP rules to train a neural network better so that a neural network not only learns from implicit correlations from the data but also from the explicit complex semantic constraints expressed by the rules.

Abstract Action languages are formal models of parts of natural language that are designed to describe effects of actions. Many of these languages can be viewed as high-level notations of answer set programs structured to represent transition systems. However, the form of answer set programs considered in the earlier work is quite limited in comparison with the modern Answer Set Programming (ASP) language, which allows several useful constructs for knowledge representation, such as choice rules, aggregates and abstract constraint atoms. We propose a new action language called BC +, which closes the gap between action languages and the modern ASP language. The main idea is to define the semantics of BC + in terms of general stable model semantics for propositional formulas, under which many modern ASP language constructs can be identified with shorthands for propositional formulas. Language BC + turns out to be sufficiently expressive to encompass the best features of other action languages, such as languages B , C , C + and BC . Computational methods available in ASP solvers are readily applicable to compute BC +, which led to an implementation of the language by extending system cplus2asp .

Abstract To be responsive to dynamically changing real-world environments, an intelligent agent needs to perform complex sequential decision-making tasks that are often guided by commonsense knowledge. The previous work on this line of research led to the framework calledinterleaved commonsense reasoning and probabilistic planning(icorpp), which used P-log for representing commmonsense knowledge and Markov Decision Processes (MDPs) or Partially Observable MDPs (POMDPs) for planning under uncertainty. A main limitation of icorppis that its implementation requires non-trivial engineering efforts to bridge the commonsense reasoning and probabilistic planning formalisms. In this paper, we present a unified framework to integrate icorpp’s reasoning and planning components. In particular, we extend probabilistic action languagepBC+ to express utility, belief states, and observation as in POMDP models. Inheriting the advantages of action languages, the new action language provides an elaboration tolerant representation of POMDP that reflects commonsense knowledge. The idea led to the design of the systempbcplus2pomdp, which compiles apBC+ action description into a POMDP model that can be directly processed by off-the-shelf POMDP solvers to compute an optimal policy of thepBC+ action description. Our experiments show that it retains the advantages of icorppwhile avoiding the manual efforts in bridging the commonsense reasoner and the probabilistic planner.

Abstract We present a probabilistic extension of action language ${\cal BC}$+$ . Just like ${\cal BC}$+$ is defined as a high-level notation of answer set programs for describing transition systems, the proposed language, which we callp ${\cal BC}$+$ , is defined as a high-level notation of LPMLNprograms—a probabilistic extension of answer set programs. We show how probabilistic reasoning about transition systems, such as prediction, postdiction, and planning problems, as well as probabilistic diagnosis for dynamic domains, can be modeled inp ${\cal BC}$+$ and computed using an implementation of LPMLN.

Abstract Logic Programs with Ordered Disjunction (LPOD) is an extension of standard answer set programs to handle preference using the construct of ordered disjunction, and CR-Prolog2is an extension of standard answer set programs with consistency restoring rules and LPOD-like ordered disjunction. We present reductions of each of these languages into the standard ASP language, which gives us an alternative way to understand the extensions in terms of the standard ASP language.

LPMLN is a recently introduced formalism that extends answer set programs by adopting the log-linear weight scheme of Markov Logic. This paper investigates the relationships between LPMLN and two other extensions of answer set programs: weak constraints to express a quantitative preference among answer sets, and P-log to incorporate probabilistic uncertainty. We present a translation of LPMLN into programs with weak constraints and a translation of P-log into LPMLN, which complement the existing translations in the opposite directions. The first translation allows us to compute the most probable stable models (i.e., MAP estimates) of LPMLN programs using standard ASP solvers. This result can be extended to other formalisms, such as Markov Logic, ProbLog, and Pearl's Causal Models, that are shown to be translatable into LPMLN. The second translation tells us how probabilistic nonmonotonicity (the ability of the reasoner to change his probabilistic model as a result of new information) of P-log can be represented in LPMLN, which yields a way to compute P-log using standard ASP solvers and MLN solvers.

Abstract Both hybrid automata and action languages are formalisms for describing the evolution of dynamic systems. This paper establishes a formal relationship between them. We show how to succinctly represent hybrid automata in an action language which in turn is defined as a high-level notation for answer set programming modulo theories—an extension of answer set programs to the first-order level similar to the way satisfiability modulo theories (SMT) extends propositional satisfiability (SAT). We first show how to represent linear hybrid automata with convex invariants by an action language modulo theories. A further translation into SMT allows for computing them using SMT solvers that support arithmetic over reals. Next, we extend the representation to the general class of non-linear hybrid automata allowing even non-convex invariants. We represent them by an action language modulo ordinary differential equations, which can be compiled into satisfiability modulo ordinary differential equations. We present a prototype systemcplus2aspmtbased on these translations, which allows for a succinct representation of hybrid transition systems that can be computed effectively by the state-of-the-art SMT solverdReal.

Abstract LPMLN is a recent addition to probabilistic logic programming languages. Its main idea is to overcome the rigid nature of the stable model semantics by assigning a weight to each rule in a way similar to Markov Logic is defined. We present two implementations of LPMLN, lpmln2asp and lpmln2mln. System lpmln2asp translates LPMLN programs into the input language of answer set solver clingo, and using weak constraints and stable model enumeration, it can compute most probable stable models as well as exact conditional and marginal probabilities. System lpmln2mln translates LPMLN programs into the input language of Markov Logic solvers, such as alchemy, tuffy, and rockit, and allows for performing approximate probabilistic inference on LPMLN programs. We also demonstrate the usefulness of the LPMLN systems for computing other languages, such as ProbLog and Pearl's Causal Models, that are shown to be translatable into LPMLN.

Action languages are formal models of parts of natural language that are designed to describe effects of actions. Many of these languages can be viewed as high level notations of answer set programs structured to represent transition systems. However, the form of answer set programs considered in the earlier work is quite limited in comparison with the modern Answer Set Programming (ASP) language, which allows several useful constructs for knowledge representation, such as choice rules, aggregates, and abstract constraint atoms. We propose a new action language called BC+, which closes the gap between action languages and the modern ASP language. Language BC+ is defined as a high level notation of propositional formulas under the stable model semantics. Due to the generality of the underlying language, BC+ is expressive enough to encompass many modern ASP language constructs and the best features of several other action languages, such as B, C, C+ and BC. Computational methods available in ASP solvers are readily applicable to compute BC+, which led us to implement the language by extending system Cplus2ASP.

We present a probabilistic extension of logic programs under the stable model semantics, inspired by the concept of Markov Logic Networks. The proposed language takes advantage of both formalisms in a single framework, allowing us to represent commonsense reasoning problems that require both logical and probabilistic reasoning in an intuitive and elaboration tolerant way.

Abstract Several extensions of the stable model semantics are available to describe ‘intensional’ functions—functions that can be described in terms of other functions and predicates by logic programs. Such functions are useful for expressing inertia and default behaviors of systems, and can be exploited for alleviating the grounding bottleneck involving functional fluents. However, the extensions were defined in different ways under different intuitions. In this paper we provide several reformulations of the extensions, and note that they are in fact closely related to each other and coincide on large syntactic classes of logic programs.

Temporal Action Logics (TAL) is a class of temporal logics for reasoning about actions. We present a reformulation of TAL in Answer Set Programming (ASP), and discuss some synergies it brings. First, the reformulation provides a means to compute TAL using efficient answer set solvers. Second, TAL provides a structured high-level language for ASP (possibly with constraint solving). Third, the reformulation allows us to compute integration of TAL and ontologies using answer set solvers, and we illustrate its usefulness in the healthcare domain in the context of medical expert systems.

Circumscription and logic programs under the stable model semantics are two well-known nonmonotonic formalisms. The former has served as a basis of classical logic based action formalisms, such as the situation calculus, the event calculus and temporal action logics; the latter has served as a basis of a family of action languages, such as language A and several of its descendants. Based on the discovery that circumscription and the stable model semantics coincide on a class of canonical formulas, we reformulate the situation calculus and the event calculus in the general theory of stable models. We also present a translation that turns the reformulations further into answer set programs, so that efficient answer set solvers can be applied to compute the situation calculus and the event calculus.

Abstract The module theorem by Janhunen et al. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets. The theorem is useful in the analysis of answer set programs, and is a basis of incremental grounding and reactive answer set programming. We extend the module theorem to the general theory of stable models by Ferraris et al. The generalization applies to non-ground logic programs allowing useful constructs in answer set programming, such as choice rules, the count aggregate, and nested expressions. Our extension is based on relating the module theorem to the symmetric splitting theorem by Ferraris et al. Based on this result, we reformulate and extend the theory of incremental answer set computation to a more general class of programs.

Abstract Nonmonotonic causal logic, introduced by McCain and Turner (McCain, N. and Turner, H. 1997. Causal theories of action and change. In Proceedings of National Conference on Artificial Intelligence (AAAI), Stanford, CA, 460–465) became the basis for the semantics of several expressive action languages. McCain's embedding of definite propositional causal theories into logic programming paved the way to the use of answer set solvers for answering queries about actions described in such languages. In this paper we extend this embedding to nondefinite theories and to the first-order causal logic.

We provide reformulations and generalizations of both the semantics of logic programs by Faber, Leone and Pfeifer and its extension to arbitrary propositional formulas by Truszczyński. Unlike the previous definitions, our generalizations refer neither to grounding nor to fixpoints, and apply to firstorder formulas containing aggregate expressions. In the same spirit as the first-order stable model semantics proposed by Ferraris, Lee and Lifschitz, the semantics proposed here are based on syntactic transformations that are similar to circumscription. The reformulations provide useful insights into the FLP semantics and its relationship to circumscription and the first-order stable model semantics.

Abstract Using the notion of an elementary loop, Gebser and Schaub (2005. Proceedings of the Eighth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'05), 53–65) refined the theorem on loop formulas attributable to Lin and Zhao (2004) by considering loop formulas of elementary loops only. In this paper, we reformulate the definition of an elementary loop, extend it to disjunctive programs, and study several properties of elementary loops, including how maximal elementary loops are related to minimal unfounded sets. The results provide useful insights into the stable model semantics in terms of elementary loops. For a nondisjunctive program, using a graph-theoretic characterization of an elementary loop, we show that the problem of recognizing an elementary loop is tractable. On the other hand, we also show that the corresponding problem is coNP-complete for a disjunctive program. Based on the notion of an elementary loop, we present the class of Head-Elementary-loop-Free (HEF) programs, which strictly generalizes the class of Head-Cycle-Free (HCF) programs attributable to Ben-Eliyahu and Dechter (1994. Annals of Mathematics and Artificial Intelligence 12, 53–87). Like an HCF program, an HEF program can be turned into an equivalent nondisjunctive program in polynomial time by shifting head atoms into the body.

We show how the situation calculus can be reformulated in terms of the first-order stable model semantics. A further transformation into answer set programs allows us to use an answer set solver to perform propositional reasoning about the situation calculus. We also provide an ASP style encoding method for Reiter's basic action theories, which tells us how the solution to the frame problem in ASP is related to the solution in the situation calculus.

The advent of emerging technologies such as Web services, service-oriented architecture, and cloud computing has enabled us to perform business services more efficiently and effectively. However, we still suffer from unintended security leakages by unauthorized services while providing more convenient services to Internet users through such a cutting-edge technological growth. Furthermore, designing and managing Web access control policies are often error-prone due to the lack of logical and formal foundation. In this paper, we attempt to introduce a logic-based policy management approach for Web access control policies especially focusing on XACML (eXtensible Access Control Markup Language) policies, which have become the de facto standard for specifying and enforcing access control policies for various applications and services in current Web-based computing technologies. Our approach adopts Answer Set Programming (ASP) to formulate XACML that allows us to leverage the features of ASP solvers in performing various logical reasoning and analysis tasks such as policy verification, comparison and querying. In addition, we propose a policy analysis method that helps identify policy violations in XACML policies accommodating the notion of constraints in role-based access control (RBAC). We also discuss a proof-of-concept implementation of our method called XACMLl2ASP with the evaluation of several XACML policies from real-world software systems.