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Research in robotic planning with temporal logic specifications, such as Linear Temporal Logic (LTL), has relied on single formulas. However, as task complexity increases, LTL formulas become lengthy, making them difficult to interpret and…
A predicate linear temporal logic LTL_{\lambda,=} without quantifiers but with predicate abstraction mechanism and equality is considered. The models of LTL_{\lambda,=} can be naturally seen as the systems of pebbles (flexible constants)…
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
In tabular prediction tasks, tree-based models combined with automated feature engineering methods often outperform deep learning approaches that rely on learned representations. While these feature engineering techniques are effective,…
This paper presents a complete axiomatization of Monadic Second-Order Logic (MSO) over infinite trees. MSO on infinite trees is a rich system, and its decidability ("Rabin's Tree Theorem") is one of the most powerful known results…
Complexity classes such as $\#\mathbf{P}$, $\oplus\mathbf{P}$, $\mathbf{GapP}$, $\mathbf{OptP}$, $\mathbf{NPMV}$, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in…
The \it{Ambient Logic} (AL) has been proposed for expressing properties of process mobility in the calculus of Mobile Ambients (MA), and as a basis for query languages on semistructured data. We study some basic questions concerning the…
Many logical properties are known to be undecidable for normal modal logics, with few exceptions such as consistency and coincidence with $\mathsf{K}$. This paper shows that the property of being a union-splitting in…
In this paper, we introduce a hybrid zonotope-based approach for formally verifying the behavior of autonomous systems operating under Linear Temporal Logic (LTL) specifications. In particular, we formally verify the LTL formula by…
In this paper we give automata-based representation of LTL-FO$^+$ properties. LTL-FO$^+$ is an extension of LTL that includes first-order quantification over bounded variable, thus greatly increasing the expressivity of the language. An…
Adding propositional quantification to the modal logics K, T or S4 is known to lead to undecidability but CTL with propositional quantification under the tree semantics (tQCTL) admits a non-elementary Tower-complete satisfiability problem.…
We present an elementary introduction to a new logic for reasoning about behaviors that occur over time. This logic is based on temporal type theory. The syntax of the logic is similar to the usual first-order logic; what differs is the…
We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…
Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with…
Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for…
In critical situations involving discrimination, gender inequality, economic damage, and even the possibility of casualties, machine learning models must be able to provide clear interpretations for their decisions. Otherwise, their obscure…
We consider modeling the conception of knowledge in terms of temporal logic. The study of knowledge logical operations is originated around 1962 by representation of knowledge and belief using modalities. Nowadays, it is very good…
This paper addresses a motion planning problem to achieve spatio-temporal-logical tasks, expressed by syntactically co-safe linear temporal logic specifications (scLTL\next), in uncertain environments. Here, the uncertainty is modeled as…
We establish a formal connection between algorithmic correspondence theory and certain dual characterization results for finite lattices, similar to Nation's characterization of a hierarchy of pseudovarieties of finite lattices,…
We present an overview on Temporal Logic Programming under the perspective of its application for Knowledge Representation and declarative problem solving. Such programs are the result of combining usual rules with temporal modal operators,…