Showing papers on "Formal language published in 2021"

Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning

Abstract: Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either small in scale or not publicly available. Thus, we construct a new large-scale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We further propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem Solver (Inter-GPS). Inter-GPS first parses the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. Unlike implicit learning in existing methods, Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step. Also, a theorem predictor is designed to infer the theorem application sequence fed to the symbolic solver for the more efficient and reasonable searching path. Extensive experiments on the Geometry3K and GEOS datasets demonstrate that Inter-GPS achieves significant improvements over existing methods. The project with code and data is available at https://lupantech.github.io/inter-gps.

PICARD: Parsing Incrementally for Constrained Auto-Regressive Decoding from Language Models

Abstract: Large pre-trained language models for textual data have an unconstrained output space; at each decoding step, they can produce any of 10,000s of sub-word tokens. When fine-tuned to target constrained formal languages like SQL, these models often generate invalid code, rendering it unusable. We propose PICARD (code available at https://github.com/ElementAI/picard), a method for constraining auto-regressive decoders of language models through incremental parsing. PICARD helps to find valid output sequences by rejecting inadmissible tokens at each decoding step. On the challenging Spider and CoSQL text-to-SQL translation tasks, we show that PICARD transforms fine-tuned T5 models with passable performance into state-of-the-art solutions.

Machine learning in tutorials – Universal applicability, underinformed application, and other misconceptions:

Abstract: Machine learning has become a key component of contemporary information systems. Unlike prior information systems explicitly programmed in formal languages, ML systems infer rules from data. This p...

Multi-agent reinforcement learning with temporal logic specifications

Abstract: In this paper, we study the problem of learning to satisfy temporal logic specifications with a group of agents in an unknown environment, which may exhibit probabilistic behaviour. From a learning perspective these specifications provide a rich formal language with which to capture tasks or objectives, while from a logic and automated verification perspective the introduction of learning capabilities allows for practical applications in large, stochastic, unknown environments. The existing work in this area is, however, limited. Of the frameworks that consider full linear temporal logic or have correctness guarantees, all methods thus far consider only the case of a single temporal logic specification and a single agent. In order to overcome this limitation, we develop the first multi-agent reinforcement learning technique for temporal logic specifications, which is also novel in its ability to handle multiple specifications. We provide correctness and convergence guarantees for our main algorithm - ALMANAC (Automaton/Logic Multi-Agent Natural Actor-Critic) - even when using function approximation. Alongside our theoretical results, we further demonstrate the applicability of our technique via a set of preliminary experiments.

SCoRe: Pre-Training for Context Representation in Conversational Semantic Parsing

Abstract: Conversational Semantic Parsing (CSP) is the task of converting a sequence of natural language queries to formal language (e.g., SQL, SPARQL) that can be executed against a structured ontology (e.g. databases, knowledge bases). To accomplish this task, a CSP system needs to model the relation between the unstructured language utterance and the structured ontology while representing the multi-turn dynamics of the dialog. Pre-trained language models (LMs) are the state-of-the-art for various natural language processing tasks. However, existing pre-trained LMs that use language modeling training objectives over free-form text have limited ability to represent natural language references to contextual structural data. In this work, we present SCORE, a new pre-training approach for CSP tasks designed to induce representations that capture the alignment between the dialogue flow and the structural context. We demonstrate the broad applicability of SCORE to CSP tasks by combining SCORE with strong base systems on four different tasks (SPARC, COSQL, MWOZ, and SQA). We show that SCORE can improve the performance over all these base systems by a significant margin and achieves state-of-the-art results on three of them. Our implementation and checkpoints of the model will be available at Anonymous URL.

A Formalisation of SysML State Machines in mCRL2

Abstract: This paper reports on a formalisation of the semi-formal modelling language SysML in the formal language mCRL2, in order to unlock formal verification and model-based testing using the mCRL2 toolset for SysML models. The formalisation focuses on a fragment of SysML used in the railway standardisation project EULYNX. It comprises the semantics of state machines, communication between objects via ports, and an action language called ASAL. It turns out that the generic execution model of SysML state machines can be elegantly specified using the rich data and process languages of mCRL2. This is a big step towards an automated translation as the generic model can be configured with a formal description of a specific set of state machines in a straightforward manner.

Formalizing Conceptual Modeling Methods with MetaMorph.

Abstract: Models evolved from mere pictures supporting human understanding to sophisticated knowledge structures processable by machines. This entails an inevitable need for computer-understandable models and languages and causes formalization to be a crucial part in the lifecycle of a modeling method. An appropriate formalism must be a means for providing a unique, unambiguous but implementation-independent way of specifying arbitrary modeling languages and for this purpose must be generic and open to capture any domain and any functionality. In this paper we give a pervasive description of the formalism MetaMorph based on predicate logic – an approach fulfilling these requirements. This is done with an extensive proof-of-concept case illustrating the application of the formalism concept by concept. For the case study we use the modeling language ProVis from the domain of stochastic education. The language ProVis comprises only few objects and relation types but with high interconnection and therefore appears as a interesting specimen for formalization and showing the feasibility of the demonstrated approach.

Implementing the formal language of the vegetation classification expert systems (ESy) in the statistical computing environment R

Abstract: Aims The machine-readable formal language of classification expert systems has become a standard for applying plot assignment rules in vegetation classification. Here we present an efficient algorithm implementing the vegetation classification expert system in the statistical programming language R. Methods The principal idea of the R implementation is to solve the assignments to vegetation types not sequentially plot by plot but to parse the assignment rules into (nested) components that each can be evaluated by simultaneous vector-based processing of all plots in a database. Results and conclusions We demonstrate the algorithm taking the EUNIS classification expert system of European habitat types (EUNIS-ESy) as an example. The R code version of the vegetation classification expert system is particularly useful in large vegetation-plot databases because it solves all logical operations vector-wise across all plots, allowing for efficient evaluation of membership expressions and formulas. Another advantage of the R implementation is that membership formulas are not only readable but can also be produced as a machine-written result, for example as the output of classification algorithms run in R.

Pyformlang: An Educational Library for Formal Language Manipulation

Abstract: Formal languages are widely studied, taught and used in computer science. However, only a small part of this domain is brought to a broader audience, and students often have no practical experience in their curriculum. In this tool paper, we introduce Pyformlang, a practical and pedagogical Python library for formal languages. Our library implements the most common algorithms of the domain, accessible by an easy-to-use interface. The code is written exclusively in Python3, with a clear structure, so as to allow students to play and learn with it.

Hilbert words as arrays generated with P systems

Abstract: Construction of finite grammars to generate languages of digitized picture patterns, considered as arrays of symbols, has been a problem of interest in two-dimensional formal languages. On the other hand, in the area of membrane computing, P systems were developed for handling the problem of picture array generation, with the rewriting involved being sequential or parallel. We introduce in this paper the array representation for the Hilbert words, the finite approximations of the Hilbert space-filling curve, and we generate them with array-rewriting rules in P systems. The array rewriting is done in parallel, with the P system serving as a control mechanism. A main contribution is the proof of correctness which is done using a linearization procedure. In addition, the advantage of the P system used is that the number of membranes involved is small (only one or two).

Polygrammar: Grammar for Digital Polymer Representation and Generation.

Abstract: Polymers are widely-studied materials with diverse properties and applications determined by different molecular structures. It is essential to represent these structures clearly and explore the full space of achievable chemical designs. However, existing approaches are unable to offer comprehensive design models for polymers because of their inherent scale and structural complexity. Here, we present a parametric, context-sensitive grammar designed specifically for the representation and generation of polymers. As a demonstrative example, we implement our grammar for polyurethanes. Using our symbolic hypergraph representation and 14 simple production rules, our PolyGrammar is able to represent and generate all valid polyurethane structures. We also present an algorithm to translate any polyurethane structure from the popular SMILES string format into our PolyGrammar representation. We test the representative power of PolyGrammar by translating a dataset of over 600 polyurethane samples collected from literature. Furthermore, we show that PolyGrammar can be easily extended to the other copolymers and homopolymers such as polyacrylates. By offering a complete, explicit representation scheme and an explainable generative model with validity guarantees, our PolyGrammar takes an important step toward a more comprehensive and practical system for polymer discovery and exploration. As the first bridge between formal languages and chemistry, PolyGrammar also serves as a critical blueprint to inform the design of similar grammars for other chemistries, including organic and inorganic molecules.

An Extended Account of Trace-relating Compiler Correctness and Secure Compilation

Abstract: Compiler correctness, in its simplest form, is defined as the inclusion of the set of traces of the compiled program in the set of traces of the original program. This is equivalent to the preservation of all trace properties. Here, traces collect, for instance, the externally observable events of each execution. However, this definition requires the set of traces of the source and target languages to be the same, which is not the case when the languages are far apart or when observations are fine-grained. To overcome this issue, we study a generalized compiler correctness definition, which uses source and target traces drawn from potentially different sets and connected by an arbitrary relation. We set out to understand what guarantees this generalized compiler correctness definition gives us when instantiated with a non-trivial relation on traces. When this trace relation is not equality, it is no longer possible to preserve the trace properties of the source program unchanged. Instead, we provide a generic characterization of the target trace property ensured by correctly compiling a program that satisfies a given source property, and dually, of the source trace property one is required to show to obtain a certain target property for the compiled code. We show that this view on compiler correctness can naturally account for undefined behavior, resource exhaustion, different source and target values, side channels, and various abstraction mismatches. Finally, we show that the same generalization also applies to many definitions of secure compilation, which characterize the protection of a compiled program linked against adversarial code.

Speech acts in mathematics

Abstract: We offer a novel picture of mathematical language from the perspective of speech act theory. There are distinct speech acts within mathematics (not just assertions), and, as we intend to show, distinct illocutionary force indicators as well. Even mathematics in its most formalized version cannot do without some such indicators. This goes against a certain orthodoxy both in contemporary philosophy of mathematics (which tends to see mathematics as a realm in which no pragmatic features of ordinary language are present) and in speech act theory (which tends to pay attention solely to communication in ordinary language but not to formal languages). As we will comment, the recognition of distinct illocutionary acts within logic and mathematics and the incorporation of illocutionary force indicators in the formal language for both goes back to Frege’s conception of these topics. We are, therefore, going back to a Fregean perspective. This paper is part of a larger project of applying contemporary speech act theory to the scientific language of mathematics in order to uncover the varieties and regular combinations of illocutionary acts (silently) present in it. For reasons of space, we here concentrate only on assertive and declarative acts within mathematics, leaving the investigation of other kinds of acts for a future occasion.

Solving String Constraints With Regex-Dependent Functions Through Transducers With Priorities And Variables.

Abstract: Regular expressions are a classical concept in formal language theory. Regular expressions in programming languages (RegEx) such as JavaScript, feature non-standard semantics of operators (e.g. greedy/lazy Kleene star), as well as additional features such as capturing groups and references. While symbolic execution of programs containing RegExes appeals to string solvers natively supporting important features of RegEx, such a string solver is hitherto missing. In this paper, we propose the first string theory and string solver that natively provide such a support. The key idea of our string solver is to introduce a new automata model, called prioritized streaming string transducers (PSST), to formalize the semantics of RegEx-dependent string functions. PSSTs combine priorities, which have previously been introduced in prioritized finite-state automata to capture greedy/lazy semantics, with string variables as in streaming string transducers to model capturing groups. We validate the consistency of the formal semantics with the actual JavaScript semantics by extensive experiments. Furthermore, to solve the string constraints, we show that PSSTs enjoy nice closure and algorithmic properties, in particular, the regularity-preserving property (i.e., pre-images of regular constraints under PSSTs are regular), and introduce a sound sequent calculus that exploits these properties and performs propagation of regular constraints by means of taking post-images or pre-images. Although the satisfiability of the string constraint language is undecidable, we show that our approach is complete for the so-called straight-line fragment. We evaluate the performance of our string solver on over 195000 string constraints generated from an open-source RegEx library. The experimental results show the efficacy of our approach, drastically improving the existing methods in both precision and efficiency.

Security and privacy with K-step opacity for finite automata via a novel algebraic approach:

Abstract: As an important secretive attribute, opacity of cyber-physical systems (CPSs) has attracted considerable attention. Existing works on opacity mainly concentrate on the formal language method by ass...

AND does not mean OR: Using Formal Languages to Study Language Models’ Representations

Abstract: A current open question in natural language processing is to what extent language models, which are trained with access only to the form of language, are able to capture the meaning of language. This question is challenging to answer in general, as there is no clear line between meaning and form, but rather meaning constrains form in consistent ways. The goal of this study is to offer insights into a narrower but critical subquestion: Under what conditions should we expect that meaning and form covary sufficiently, such that a language model with access only to form might nonetheless succeed in emulating meaning? Focusing on several formal languages (propositional logic and a set of programming languages), we generate training corpora using a variety of motivated constraints, and measure a distributional language model’s ability to differentiate logical symbols (AND, OR, and NOT). Our findings are largely negative: none of our simulated training corpora result in models which definitively differentiate meaningfully different symbols (e.g., AND vs. OR), suggesting a limitation to the types of semantic signals that current models are able to exploit.

Finite-Word Hyperlanguages

Abstract: Formal languages are in the core of models of computation and their behavior. A rich family of models for many classes of languages have been widely studied. Hyperproperties lift conventional trace-based languages from a set of execution traces to a set of sets of executions. Hyperproperties have been shown to be a powerful formalism for expressing and reasoning about information-flow security policies and important properties of cyber-physical systems. Although there is an extensive body of work on formal-language representation of trace properties, we currently lack such a general characterization for hyperproperties. We introduce hyperlanguages over finite words and models for expressing them. Essentially, these models express multiple words by using assignments to quantified word variables. Relying on the standard models for regular languages, we propose hyperregular expressions and finite-word hyperautomata (NFH), for modeling the class of regular hyperlanguages. We demonstrate the ability of regular hyperlanguages to express hyperproperties for finite traces. We explore the closure properties and the complexity of the fundamental decision problems such as nonemptiness, universality, membership, and containment for various fragments of NFH.

Solomon Marcus Contributions to Theoretical Computer Science and Applications

Abstract: Solomon Marcus (1925–2016) was one of the founders of the Romanian theoretical computer science. His pioneering contributions to automata and formal language theories, mathematical linguistics and natural computing have been widely recognised internationally. In this paper we briefly present his publications in theoretical computer science and related areas, which consist in almost ninety papers. Finally we present a selection of ten Marcus books in these areas.

New ideas for brain modelling 5

Abstract: This paper describes a process for combining patterns and features, to guide a search process and make predictions. It is based on the functionality that a human brain might have, which is a highly distributed network of simple neuronal components that can apply some level of matching and cross-referencing over retrieved patterns. The process uses memory in a dynamic way and it is directed through the pattern matching. The paper firstly describes the mechanisms for neuronal search, memory and prediction. The paper then presents a formal language (Cognitive Process Language) for defining cognitive processes, that is, pattern-based sequences and transitions. The language can define an outer framework for concept sets that are linked to perform the act. The language also has a mathematical basis, allowing for the rule construction to be consistent. The CPL is novel in some ways. Firstly, it uses 3 entities for each statement, where the object source is also required. This roots the act and allows for cross-referencing that can create a behaviour script automatically. It also allows natural cycles to be derived from the script that can define the brain-like processes. Now, both static memory and dynamic process hierarchies can be built as tree structures. A theory about linking can suggest that nodes in different regions link together when generally they represent the same thing.

Properties of Graphs Specified by a Regular Language.

Abstract: Traditionally, graph algorithms get a single graph as input, and then they should decide if this graph satisfies a certain property \(\varPhi \). What happens if this question is modified in a way that we get a possibly infinite family of graphs as an input, and the question is if there exists one graph satisfying \(\varPhi \)? We approach this question by using formal languages for specifying families of graphs. In particular, we show that certain graph properties can be decided by studying the syntactic monoid of the specification language.

Essence of grammar according to modern linguistics and Afghan linguists’ perspectives

Abstract: The paper explored views in modern linguistic theories and Afghan linguist perspectives about essence of grammar, its original source, its function in language use and the relationship between mental rules and their description in grammar books. The data were collected from theoretical linguistics, grammar books and 10 Afghan professors who teach linguistics and Persian-Dari grammar in Kabul University via a questionnaire. MS excel was used to analyze the data. The results show the term Grammar refers to a set of constructional rules of a language located in speakers’ minds. It is unconscious knowledge which enables speakers of a language to produce and understand its utterances. These mental rules govern composition of phonemes, morphemes, words, phrases, clauses and sentences. Grammar books are like maps of original grammar which has mental essence and describe it. Children learn their native language from elders and their coeval speakers. Second language learners, can learn a foreign language through social interaction and grammar books. Compiling grammatical rules of a language introduces word formation techniques to expand its lexicon, help speakers to know more about their language capacities and possibilities. Grammar books aim to facilitate learning formal language, description of constructional rules, language learning for foreigners and provide correct writing guidelines. The research prescribes grammar teachers to use grammar as means of enrichment of formal language, as it can better function to do its scientific mission.

Evaluating the Correctness of Explainable AI Algorithms for Classification.

Abstract: Explainable AI has attracted much research attention in recent years with feature attribution algorithms, which compute "feature importance" in predictions, becoming increasingly popular. However, there is little analysis of the validity of these algorithms as there is no "ground truth" in the existing datasets to validate their correctness. In this work, we develop a method to quantitatively evaluate the correctness of XAI algorithms by creating datasets with known explanation ground truth. To this end, we focus on the binary classification problems. String datasets are constructed using formal language derived from a grammar. A string is positive if and only if a certain property is fulfilled. Symbols serving as explanation ground truth in a positive string are part of an explanation if and only if they contributes to fulfilling the property. Two popular feature attribution explainers, Local Interpretable Model-agnostic Explanations (LIME) and SHapley Additive exPlanations (SHAP), are used in our experiments.We show that: (1) classification accuracy is positively correlated with explanation accuracy; (2) SHAP provides more accurate explanations than LIME; (3) explanation accuracy is negatively correlated with dataset complexity.

Consensus string problem for multiple regular languages

Abstract: The consensus string (or center string, closest string) of a set S of strings is defined as a string which is within a radius r from all strings in S. It is well-known that the consensus string problem for a finite set of equal-length strings is NP-complete. We study the consensus string problem for multiple regular languages. We define the consensus string of languages \(L_1, \ldots , L_k\) to be within distance at most r to some string in each of the languages \(L_1, \ldots , L_k\). We also study the complexity of some parameterized variants of the consensus string problem. For a constant k, we give a polynomial time algorithm for the consensus string problem for k regular languages using additive weighted finite automata. We show that the consensus string problem for multiple regular languages becomes intractable when k is not fixed. We also examine the case when the length of the consensus string is given as part of input.

Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning

Abstract: Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either small in scale or not publicly available. Thus, we construct a new large-scale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We further propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem Solver (Inter-GPS). Inter-GPS first parses the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. Unlike implicit learning in existing methods, Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step. Also, a theorem predictor is designed to infer the theorem application sequence fed to the symbolic solver for the more efficient and reasonable searching path. Extensive experiments on the Geometry3K and GEOS datasets demonstrate that Inter-GPS achieves significant improvements over existing methods. The project with code and data is available at this https URL.

Symbolic and automatic differentiation of languages

Abstract: Formal languages are usually defined in terms of set theory. Choosing type theory instead gives us languages as type-level predicates over strings. Applying a language to a string yields a type whose elements are language membership proofs describing how a string parses in the language. The usual building blocks of languages (including union, concatenation, and Kleene closure) have precise and compelling specifications uncomplicated by operational strategies and are easily generalized to a few general domain-transforming and codomain-transforming operations on predicates. A simple characterization of languages (and indeed functions from lists to any type) captures the essential idea behind language “differentiation” as used for recognizing languages, leading to a collection of lemmas about type-level predicates. These lemmas are the heart of two dual parsing implementations—using (inductive) regular expressions and (coinductive) tries—each containing the same code but in dual arrangements (with representation and primitive operations trading places). The regular expression version corresponds to symbolic differentiation, while the trie version corresponds to automatic differentiation. The relatively easy-to-prove properties of type-level languages transfer almost effortlessly to the decidable implementations. In particular, despite the inductive and coinductive nature of regular expressions and tries respectively, we need neither inductive nor coinductive/bisimulation arguments to prove algebraic properties.

Identifying Competency Demands in Calculus Textbook Examples: the Case of Integrals

Abstract: This study investigates how three widely used calculus textbooks realise integrals as a potential to prompt mathematical competencies, adapting the rating scheme used in Boesen et al. (The Journal of Mathematical Behavior, 33:72–87, 2014), Pettersen and Braeken (International Journal of Science and Mathematics Education, 17(2):405–425, 2019) and Turner, Blum and Niss (2015). For this purpose, the study analysed examples (n = 444) about integrals—specifically, to assess the extent to which solving those examples calls for the activation of a particular set of mathematical competencies: Communication; Devising Strategies; Mathematising; Representation; Using Symbols, Operations and Formal Language [Symbols and Formalism]; Reasoning and Argument. The competency demand of the examples was also identified on a scale from 0 (lowest demand) to 3 (highest demand) for each of six mathematical competencies. The findings revealed substantial similarities among the three calculus textbooks with regard to the level of competency demands: high level of Communication and Symbols and Formalism and low level of Devising Strategies, Representation, Reasoning and Argument and Mathematising. Relationships between these findings, implementations and future research directions are also discussed.