Related papers: Characterization of Strongly Equivalent Logic Prog…
Epistemic Logic Programs (ELPs), that is, Answer Set Programming (ASP) extended with epistemic operators, have received renewed interest in recent years, which led to a flurry of new research, as well as efficient solvers. An important…
We define a Kripke semantics for a conditional logic based on the propositional logic $\mathsf{N4}$, the paraconsistent variant of Nelson's logic of strong negation; we axiomatize the minimal system induced by this semantics. The resulting…
We investigate some well-known (and a few not-so-well-known) many-valued logics that have a small number (3 or 4) of truth values. For some of them we complain that they do not have any \emph{logical} use (despite their perhaps having some…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…
The multi-valued logic of {\L}ukasiewicz is a substructural logic that has been widely studied and has many interesting properties. It is classical, in the sense that it admits the axiom schema of double negation, [DNE]. However, our…
The model theory of a first-order logic called N^4 is introduced. N^4 does not eliminate double negations, as classical logic does, but instead reduces fourfold negations. N^4 is very close to classical logic: N^4 has two truth values;…
The sequential composition of propositional logic programs has been recently introduced. This paper studies the sequential {\em decomposition} of programs by studying Green's relations $\mathcal{L,R,J}$ -- well-known in semigroup theory --…
Logic programs with ordered disjunction (LPODs) combine ideas underlying Qualitative Choice Logic (Brewka et al. KR 2002) and answer set programming. Logic programming under answer set semantics is extended with a new connective called…
A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…
It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the…
Large language models perform well on many logical reasoning benchmarks, but it remains unclear which core logical skills they truly master. To address this, we introduce LogicSkills, a benchmark that isolates three fundamental logical…
Neural-symbolic integration aims to combine the connectionist subsymbolic with the logical symbolic approach to artificial intelligence. In this paper, we first define the answer set semantics of (boolean) neural nets and then introduce…
A recent framework of relativized hyperequivalence of programs offers a unifying generalization of strong and uniform equivalence. It seems to be especially well suited for applications in program optimization and modular programming due to…
Cumulative logics are studied in an abstract setting, i.e., without connectives, very much in the spirit of Makinson's early work. A powerful representation theorem characterizes those logics by choice functions that satisfy a weakening of…
Extensional higher-order logic programming has been introduced as a generalization of classical logic programming. An important characteristic of this paradigm is that it preserves all the well-known properties of traditional logic…
We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider…
Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. In programming, short-circuit…
Logic programming has developed as a rich field, built over a logical substratum whose main constituent is a nonclassical form of negation, sometimes coexisting with classical negation. The field has seen the advent of a number of…
Closely related languages show linguistic similarities that allow speakers of one language to understand speakers of another language without having actively learned it. Mutual intelligibility varies in degree and is typically tested in…
We present a family of minimal modal logics (namely, modal logics based on minimal propositional logic) corresponding each to a different classical modal logic. The minimal modal logics are defined based on their classical counterparts in…