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In recent years, the effort to formalize erotetic inferences---i.e., inferences to and from questions---has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these…

We present a novel asynchronous hyper linear time temporal logic named LPrL (Linear Time Predicate Logic) and establish its basic theory. LPrL is a natural first order extension of LTL (Linear time temporal logic), in which the predicates…

Separation logic is successful for software verification of heap-manipulating programs. Numbers are necessary to be added to separation logic for verification of practical software where numbers are important. However, properties of the…

In this paper, we show that the derivability problem for the primal propositional logic remains solvable in polynomial time upon adding a certain form of the principle of equivalent form substitution; and that, upon adding another form of…

Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are…

We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation…

Learning and logic are distinct and remarkable approaches to prediction. Machine learning has experienced a surge in popularity because it is robust to noise and achieves high performance; however, ML experiences many issues with knowledge…

We propose a "formula slicing" method for finding inductive invariants. It is based on the observation that many loops in the program affect only a small part of the memory, and many invariants which were valid before a loop are still valid…

In a seminal paper from 1985, Sistla and Clarke showed that the model-checking problem for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If, in contrast, the set of…

Standpoint linear temporal logic SLTL is a recent formalism able to model possibly conflicting commitments made by distinct agents, taking into account aspects of temporal reasoning. In this paper, we analyse the computational properties of…

Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…

Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…

We study implicational formulas in the context of proof complexity of intuitionistic propositional logic (IPC). On the one hand, we give an efficient transformation of tautologies to implicational tautologies that preserves the lengths of…

We address the separability problem for straight-line string constraints. The separability problem for languages of a class C by a class S asks: given two languages A and B in C, does there exist a language I in S separating A and B (i.e.,…

The logic of bunched implication BI provides a framework for reasoning about resource composition and forms the basis for an assertion language of separation logic which is used to reason about software programs. Propositional BI is…

We survey systematic approaches to basis-restricted fragments of propositional logic and modal logics, with an emphasis on how expressive power and computational complexity depend on the allowed operators. The propositional case is…

This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…

We present probabilistic logic programming under inheritance with overriding. This approach is based on new notions of entailment for reasoning with conditional constraints, which are obtained from the classical notion of logical entailment…

The logic of bunched implications (BI), introduced by O'Hearn and Pym (1999), has attracted significant attention due to its elegant proof calculus, varied semantics, and close connections to the propositional fragment of separation logic.…

In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) v D,…