Related papers: Horn Clauses in Hybrid-Dynamic First-Order Logic

If we replace first order logic by second order logic in the original definition of G\"odel's inner model $L$, we obtain HOD. In this paper we consider inner models that arise if we replace first order logic by a logic that has some, but…

The relevance of polynomial formula classes to deductive efficiency motivated their search, and currently, a great number of such classes is known. Nonetheless, they have been exclusively sought in the setting of clausal form and…

Functional programming comes in two flavours: one where ``functions are first-class citizens'' (we call this applicative) and one which is based on equations (we call this declarative). In relational programming clauses play the role of…

We propose $\mathcal{E}^{\downarrow}$-logic as a formal foundation for the specification and development of event-based systems with local data states. The logic is intended to cover a broad range of abstraction levels from abstract…

We introduce a quantum analogue of classical first-order logic (FO) and develop a theory of quantum first-order logic as a basis of the productive discussions on the power of logical expressiveness toward quantum computing. The purpose of…

This paper investigates first-order game logic and first-order modal mu-calculus, which extend their propositional modal logic counterparts with first-order modalities of interpreted effects such as variable assignments. Unlike in the…

We present a theory of parameterized dynamic logic, namely DLp, for specifying and reasoning about a rich set of program models based on their transitional behaviours. Different from most dynamic logics that deal with regular expressions or…

In this paper, we prove the semantic incompleteness of the Hilbert-style system for the minimal normal term-modal logic with equality and non-rigid terms that was proposed in Liberman et al. (2020) "Dynamic Term-modal Logics for First-order…

We propose Modal Logical Neural Networks (MLNNs), a neurosymbolic framework that integrates deep learning with the formal semantics of modal logic, enabling reasoning about necessity and possibility. Drawing on Kripke semantics, we…

Dual Horn clauses mirror key properties of Horn clauses. This paper explores the ``other side of the looking glass'' to reveal some expected and unexpected symmetries and their practical uses. We revisit Dual Horn clauses as enablers of a…

This paper describes the first-order logical environment FOLE. Institutions in general, and logical environments in particular, give equivalent heterogeneous and homogeneous representations for logical systems. As such, they offer a…

Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…

We consider two-variable first-order logic on finite words with a fixed number of quantifier alternations. We show that all languages with a neutral letter definable using the order and finite-degree predicates are also definable with the…

First-order learning involves finding a clause-form definition of a relation from examples of the relation and relevant background information. In this paper, a particular first-order learning system is modified to customize it for finding…

This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…

We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…

In this paper, we present a Hoare-style logic for reasoning about quantum programs with classical variables. Our approach offers several improvements over previous work: (1) Enhanced expressivity of the programming language: Our logic…

We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…

We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…

The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…