Related papers: Adding successor: A transfer theorem for separatio…
A grammar model for concurrent, object-oriented natural language parsing is introduced. Complete lexical distribution of grammatical knowledge is achieved building upon the head-oriented notions of valency and dependency, while inheritance…
The morphological systems of natural languages are replete with examples of the same devices used for multiple purposes: (1) the same type of morphological process (for example, suffixation for both noun case and verb tense) and (2)…
In this paper we show that {\omega}B- and {\omega}S-regular languages satisfy the following separation-type theorem If L1,L2 are disjoint languages of {\omega}-words both recognised by {\omega}B- (resp. {\omega}S)-automata then there exists…
Much recent research has been devoted to modeling effects within type theory. Building on this work, we observe that effectful type theories can provide a foundation on which to build semantics for more complex programming constructs and…
We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation…
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…
Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary "propositional" logic should in general be the logic of subsets of a given universe set. Partitions on…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
We develop local reasoning techniques for message passing concurrent programs based on ideas from separation logics and resource usage analysis. We extend processes with permission- resources and define a reduction semantics for this…
We study the problem of language inclusion between finite, labeled prime event structures. Prime event structures are a formalism to compactly represent concurrent behavior of discrete systems. A labeled prime event structure induces a…
We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities.…
Modeling the structure of coherent texts is a key NLP problem. The task of coherently organizing a given set of sentences has been commonly used to build and evaluate models that understand such structure. We propose an end-to-end…
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…
Logic can be made useful for programming and for databases independently of logic programming. To be useful in this way, logic has to provide a mechanism for the definition of new functions and new relations on the basis of those given in…
Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically…
In this article, I focus on the resiliency of the P=?NP problem. The main point to deal with is the change of the underlying logic from first to second-order logic. In this manner, after developing the initial steps of this change, I can…
Crosslingual transfer is crucial to contemporary language models' multilingual capabilities, but how it occurs is not well understood. We ask what happens to a monolingual language model when it begins to be trained on a second language.…
Concurrent separation logic (CSL) is a specification logic for concurrent imperative programs with shared memory and locks. In this paper, we develop a concurrent and interactive account of the logic inspired by asynchronous game semantics.…
As transformers have gained prominence in natural language processing, some researchers have investigated theoretically what problems they can and cannot solve, by treating problems as formal languages. Exploring such questions can help…
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…