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## Proof-theoretic and Higher-order Extensions of Logic Programming

### Citations

794 | A framework for defining logics
- Harper, Honsell, et al.
- 1993
(Show Context)
Citation Context ... is named HOHF; with H f OHF we denote its restriction to quantification over variable and function symbols, that is o is only allowed as a range type. Examples of H f OHF are Miller’s Lλ [45] and LF =-=[39]-=-. FOHF is the further restriction to first-order quantification. We now introduce a focused version of the uniform proofs system of [51] (Fig. 1); it defines the following judgements, where Γ contains... |

419 | Logic Programming with Focusing Proofs in Linear Logic, - Andreoli - 1992 |

340 | Logic programming in a fragment of intuitionistic linear logic.
- Hodas, Miller
- 1994
(Show Context)
Citation Context ...llow suit. In his 1990 thesis Andreoli established the foundation of focusing proofs in linear logic [2]. In 1991 the uniform proof approach was extended to linear logic programming by Miller & Hodas =-=[41]-=-. We start with the logic underlying λProlog.Proof-Theoretic and Higher-Order Extensions of Logic Programming 259 Σ : Γ −→ ⊤ ⊢⊤ Σ : Γ −→ G1 Σ : Γ −→ G1 ∧ G2 Σ : Γ −→ G2 ⊢∧ Σ :(Γ, D) −→ G ⊢⊃ Σ : Γ −→ ... |

314 | A Logic Programming Language with Lambda-abstraction, Function Variables, and Simple Unification
- Miller
- 1991
(Show Context)
Citation Context ...ove language is named HOHF; with H f OHF we denote its restriction to quantification over variable and function symbols, that is o is only allowed as a range type. Examples of H f OHF are Miller’s Lλ =-=[45]-=- and LF [39]. FOHF is the further restriction to first-order quantification. We now introduce a focused version of the uniform proofs system of [51] (Fig. 1); it defines the following judgements, wher... |

234 | A linear logical framework.
- Cervesato, Pfenning
- 1996
(Show Context)
Citation Context ...ible intuitionistic dynamic assumptions and ∆, containing the linear ones, seen as a multiset. Notice that while Lolli is first-order, its type-theoretic counterpart, the Linear Logical Framework LLF =-=[23]-=-, has functional quantification; however, they have the same proof search aspects, safe from linear unification, as we detail in Section 3.2. Σ : Γ; ∆ −→ G Clauses Γ; ∆ under signature Σ uniformly ent... |

206 | Linear objects: Logical processes with built-in inheritance.
- Andreoli, Pareschi
- 1991
(Show Context)
Citation Context ...ause of perm/1, we generate, upon backtracking, all permutations of the given list. Hence the main reverse predicate selects the first solution with the meta-predicate once/1. ⋄ 2.3 LO Linear Objects =-=[4, 5]-=- was the first proposal for a linear logic programming language. It extends Horn logic by generalizing clause heads to multisets of atoms connected by multiplicative disjunction (�), i.e. clauses have... |

166 |
A Logical Analysis of Modules in Logic Programming.
- Miller
- 1989
(Show Context)
Citation Context ...er λProlog to Reflective Prolog [27]. She and coauthors went on investigating applications of the language for example to program transformations [7]. Independently, Momigliano [52] extended Miller’s =-=[46]-=-, providing a way of encoding via the double negation translation of all classical logic into a focused uniform system. The language was FOHF, but the approach would apply to H f OHF as well. In [53] ... |

165 | Higher-order logic programming.
- Miller, Nadathur
- 1986
(Show Context)
Citation Context ...ects that pertain to the computational level and allowing us to reason about them logically. A paradigmatic example of DAC is Miller et al’s approach, which led to λProlog in the late 80’s. The paper =-=[47]-=- clearly illustrates the basic ideas, starting from a precise notion of uniform proofs (to be defined shortly) and characterizing as “abstract logic programming systems” those where each goal has a un... |

98 |
N-Prolog: An Extension of Prolog with Hypothetical Implications. II. Logical Foundations and Negation as Failure.
- Gabbay
- 1985
(Show Context)
Citation Context ...als Φ. We refer to [50] for the twenty proof rules. 3 The Italian contribution The origin of the Italian interest in proof-theoretic extensions of LP can be traced back to Gabbay and Reily’s N-Prolog =-=[33,34]-=-, which featured embedded implication in goals, but no universal quantification: free variables can be shared in an implicational goal, creating certain difficulties especially when coupled with negat... |

96 | A multiple-conclusion specification logic.
- Miller
- 1996
(Show Context)
Citation Context ...’s � can also be seen as a form of constructive disjunction yielding indefinite answers; we will touch upon this links between linear and disjunctive logic programming in Section 3.3. 2.4 Forum Forum =-=[49]-=- can be seen as the fusion of Lolli and LO and allows one to view entire linear logic as an abstract LP language. Indeed, simply adding multiplicative falsity ⊥ to Lolli yields a “goal-oriented” prese... |

86 | Modularity in logic programming
- Bugliesi, Lamma, et al.
- 1994
(Show Context)
Citation Context ...ordano and others extensively researched applications w.r.t. modules and scoping constructs and extension to modal analysis, see e.g. [9]. We will not analyze this further as already well detailed in =-=[17]-=-. We will, however, briefly mention [37] that fixes some of the problems raised in [33]. The authors propose an operational semantics extending Stärk’s ESLDNF, establishing a soundness and completenes... |

68 | Implementing tactics and tacticals in a higher-order logic programming language
- Felty
- 1993
(Show Context)
Citation Context ...al could be P = (lambda x y\ reverse(x,y)), mappred(P,[[1,2],[3,4]],Ys). with answer substitution Ys = [[2,1],[4,3]]. ⋄ Although some nifty applications based on these features emerged early on, e.g. =-=[32]-=-, predicate-as-values, we argue, never managed to attain the same prominence that it has in functional programming. Functional quantification instead has had a pivotal role in the theory and practice ... |

68 | Focusing and polarization in linear, intuitionistic, and classical logics
- Liang, Miller
(Show Context)
Citation Context ...A. Momigliano and M. Ornaghi negative bias, which happens to be complete only when existentials and disjunctions are excluded from the syntax. These observation have been significantly generalized in =-=[42]-=-. However, there is another angle to “higher-order” extensions to which we have not done justice yet: work related to languages based on some form of λ-calculus. This is indeed the second way a langua... |

67 | Efficient resource management for linear logic proof search
- Cervesato, Hodas, et al.
(Show Context)
Citation Context ... to be just an instance of a more general resource management problem in linear logic programming (and, with a somewhat different emphasis, in linear theorem proving). As pointed out and addressed in =-=[21]-=-, a properly understood operational semantics has to deal with two additional features. First, the ⊤ connective is allowed to consume any resource, a feature which is handy to wind up with success cer... |

64 | Lexical scoping as universal quantification
- Miller
- 1989
(Show Context)
Citation Context ...ract logic programming256 A. Momigliano and M. Ornaghi language is then a logical system for which uniform proofs are complete. To make our discussion more concrete we consider an example taken from =-=[44]-=-, illustrating scoping and modularity. Example 1. Consider the well known Prolog reverse program; reverse(L,R) :- r(L,R,[]). r([],Ys,Ys). r([X|Xs],R,Ys) :- r(Xs,R,[X|Ys]). reverse/2 uses an auxiliary ... |

63 |
Mechanizing metatheory in a logical framework
- Harper, Licata
(Show Context)
Citation Context ...y associated with negation and the OWA typical of logical frameworks. This has come to be known as the Regular World Assumption that has shown to be a central notion in inductive meta-theorem proving =-=[63, 40]-=- in systems such as Twelf [62]. 3.2 Lolli A problem specific to proof search in linear logic is how to effectively split resources when dealing with multiplicative connectives, without trying exponent... |

61 | Monadic concurrent linear logic programming
- López, Pfenning, et al.
- 2005
(Show Context)
Citation Context ...] in this volume. We remark that bottom-up evaluation has now gained an important role in general sequent-based automated theorem proving [42, 25], as well as in the operational semantics of LolliMon =-=[43]-=-, the first-order logic programming language underlying the Concurrent Logical Framework [66]. The latter integrates Lolli with a monadic modality encapsulating synchronous connectives. 3.4 Forum Some... |

49 | A Logical Characterization of Forward and Backward Chaining
- Chaudhuri, Pfenning, et al.
- 2008
(Show Context)
Citation Context ...istic logic as well. In fact, it can be shown that, for the Horn fragment, a positive bias to atoms yields hyper-resolution (forward chaining), while a negative one SLD-resolution (backward chaining) =-=[25]-=-. More in general, uniform proofs can be seen as a special case of focusing, where atoms are given negative bias, which happens to be complete only when existentials and disjunctions are excluded from... |

47 | Proof Theoretic Approach to Specification Languages
- Chirimar
- 1995
(Show Context)
Citation Context ... as the one a programmer would expect. In fact, focusing on ⊥ is rather non-informative, leading a naive interpreter into a tight and endless loop. Thus, the view of Forum as a specification language =-=[26]-=- and efforts, some of which we mention in Section 3.4, to find a meaningful sub-language amenable to a programming language interpretation. The relevant judgments comprise two-sided multi-succedent se... |

41 | A linear spine calculus
- Cervesato, Pfenning
(Show Context)
Citation Context ...lution for sequent calculi that pushes all non-determinism out of focusing and into the introduction rules. This has also applications in proof-theoretic compilation [19]. The (linear) spine calculus =-=[24]-=- is an answer to a related issue: devising an efficient representation of the (linear) λ-calculus, tailored to make building blocks of LP such as unification efficient even in the higher-order case. I... |

37 |
A Transformational Approach to Negation in Logic Programming
- Barbuti, Mancarella, et al.
- 1990
(Show Context)
Citation Context ...pply to H f OHF as well.In [53] the issue of endowing a logical framework (namely H f OHF) with a logically justified notion of negation is re-addressed, adapting the idea of elimination of negation =-=[10]-=- to the higher-order setting. This includes two separate phases. Complementing terms, i.e. in this case higher-order patterns: due the presence of partially applied λterms, intuitionistic λ-calculi ar... |

37 | The Abella Interactive Theorem Prover (System Description). In:
- Gacek
- 2008
(Show Context)
Citation Context ...f HOAS and principle of (co)induction, both in standard systems [54] and in ones directly derived from logic programming such as the Bedwyr model-checker [8] and the Abella interactive theorem prover =-=[36]-=-, see [55] for work on their logical foundations. Acknowledgments This survey owes to many of Miller’s papers, especially “An Overview of Linear Logic Programming” [50]. We thank Iliano Cervesato and ... |

31 |
Lanzarone: A Metalogic Programming Language
- Costantini, A
- 1989
(Show Context)
Citation Context ...schi then hooked up with Andreoli to develop LO as we have mentioned in Section 2.3. Miller also supervised Arcelli’s thesis [6] in Milano, where she related second-order λProlog to Reflective Prolog =-=[27]-=-. She and coauthors went on investigating applications of the language for example to program transformations [7]. Independently, Momigliano [52] extended Miller’s [46], providing a way of encoding vi... |

29 | The bedwyr system for model checking over syntactic expressions
- Baelde, Gacek, et al.
- 2007
(Show Context)
Citation Context ...concurrent ones [65, 66]. 2. The integration of HOAS and principle of (co)induction, both in standard systems [54] and in ones directly derived from logic programming such as the Bedwyr model-checker =-=[8]-=- and the Abella interactive theorem prover [36], see [55] for work on their logical foundations. Acknowledgments. This survey owes to many of Miller’s papers, especially “An Overview of Linear Logic P... |

19 |
Logic & Object–Oriented Programming in Linear Logic.
- Delzanno
- 1997
(Show Context)
Citation Context ...gio Levi and his school, in their research aiming to integrate (linear) logic programming with other paradigm such as concurrency and objectorientation, beginning with Guglielmi and Delzanno’s thesis =-=[28, 38]-=-. The latter then moved to Genoa, where he collaborated with M. Martelli, Bozzano and others. The relationship between linear and disjunctive LP mentioned in [4] is taken up in [12], where the authors... |

19 |
A linear logical framework. Information and Computation
- Cervesato, Pfenning
- 1998
(Show Context)
Citation Context ...ible intuitionistic dynamic assumptions and Δ, containing the linear ones, seen as a multiset. Notice that while Lolli is first-order, its type-theoretic counterpart, the Linear Logical Framework LLF =-=[23]-=-, has functional quantification; however, they have the same proof search aspects, safe from linear unification, as we detail in Section 3.2. Σ : Γ; Δ −→ G Clauses Γ; Δ under signature Σ uniformly ent... |

17 |
Gopalan Nadathur, and Alwen Tiu. The Bedwyr system for model checking over syntactic expressions
- Baelde, Gacek, et al.
(Show Context)
Citation Context ...concurrent ones [65, 66]. 2. The integration of HOAS and principle of (co)induction, both in standard systems [54] and in ones directly derived from logic programming such as the Bedwyr model-checker =-=[8]-=- and the Abella interactive theorem prover [36], see [55] for work on their logical foundations. Acknowledgments This survey owes to many of Miller’s papers, especially “An Overview of Linear Logic Pr... |

17 | Lo and behold! Concurrent structured processes
- Andreoli, Pareschi
- 1990
(Show Context)
Citation Context ...combinator in a language such as Standard ML: Example 2 mappred(P,[],[]). mappred(P,[X|Xs],[Y|Ys]) :- P(X,Y), mappred(P,Xs,Ys). A sample goal could be P = (lambda x y\ reverse(x,y)), mappred(P,[[1,2],=-=[3,4]-=-],Ys). with answer substitution Ys = [[2,1],[4,3]]. ⋄ Although some nifty applications based on these features emerged early on, e.g. [32], predicate-as-values, we argue, never managed to attain the s... |

15 | A.: A modal extension of logic programming: Modularity, beliefs and hypothetical reasoning
- Baldoni, Giordano, et al.
- 1998
(Show Context)
Citation Context ...e sparked a lot of interest, especially in Torino: A. Martelli, Giordano and others extensively researched applications w.r.t. modules and scoping constructs and extension to modal analysis, see e.g. =-=[9]-=-. We will not analyze this further as already well detailed in [17]. We will, however, briefly mention [37] that fixes some of the problems raised in [33]. The authors propose an operational semantics... |

15 |
Abstract Logic Programming in Linear Logic—Independence and Causality in a First Order Calculus
- Guglielmi
- 1996
(Show Context)
Citation Context ...io Levi and his school, in their research aiming to integrate (linear) logic programming with other paradigm such as concurrency and object-orientation, beginning with Guglielmi and Delzanno’s thesis =-=[38, 28]-=-. The latter then moved to Genoa, where he collaborated with M. Martelli, Bozzano and others. The relationship between linear and disjunctive LP mentioned in [4] is taken up in [12], where the authors... |

14 | R.: Abstract interpretation of linear logic programming
- Andreoli, Castagnetti, et al.
- 1993
(Show Context)
Citation Context ...combinator in a language such as Standard ML: Example 2 mappred(P,[],[]). mappred(P,[X|Xs],[Y|Ys]) :- P(X,Y), mappred(P,Xs,Ys). A sample goal could be P = (lambda x y\ reverse(x,y)), mappred(P,[[1,2],=-=[3,4]-=-],Ys). with answer substitution Ys = [[2,1],[4,3]]. ⋄ Although some nifty applications based on these features emerged early on, e.g. [32], predicate-as-values, we argue, never managed to attain the s... |

14 | Overview of Linear Logic programming
- Miller
- 2004
(Show Context)
Citation Context ...Φ Clauses Γ; Δ under signature Σ uniformly entails multisets of goals G; Φ. Σ : Γ; Δ D −→ A; Φ Focused clause D from Γ or Δ \ D under signature Σ entails multisets of atoms A and goals Φ. We refer to =-=[50]-=- for the twenty proof rules.264 A. Momigliano and M. Ornaghi 3 The Italian Contribution The origin of the Italian interest in proof-theoretic extensions of LP can be traced back to Gabbay and Reily’s... |

13 | An Effective Fixpoint Semantics for Linear Logic Programs. Theory and Practice of Logic Programming
- Bozzano, Delzanno, et al.
- 2002
(Show Context)
Citation Context ...ub-structural fragments of DLP, where contraction on the right is disallowed. More extensive connections betweena fragment of LO and DLP are further established using abstract interpretation methods =-=[13]-=-. A propositional bottom-up semantics for LO (and its extension with multiplicative unit LO1) is proposed via a fixed point operator operating on (ideals of) multisets. Note that the semantics is effe... |

13 | Proof-theoretic foundation of compilation in logic programming languages
- Cervesato
- 1998
(Show Context)
Citation Context ...siduation calculus, a form of resolution for sequent calculi that pushes all non-determinism out of focusing and into the introduction rules. This has also applications in proof-theoretic compilation =-=[19]-=-. The (linear) spine calculus [24] is an answer to a related issue: devising an efficient representation of the (linear) λ-calculus, tailored to make building blocks of LP such as unification efficien... |

12 | Petri Nets and Linear Logic: a Case Study for Logic Programming
- Cervesato
- 1995
(Show Context)
Citation Context ... a monadic modality encapsulating synchronous connectives. 3.4 Forum Some early work exploited the connection between linear logic and multiset rewriting to encode aspects of planning and concurrency =-=[15, 18]-=-. More developed research was concerned with finding a logical counterpart of object-based languages such as the Object Calculus; [16] introduced Ob⊸, an object language where methods are represented ... |

12 | Linear higher-order pre-unification
- Cervesato, Pfenning
(Show Context)
Citation Context ...defines the following judgements, where Γ contains the program and the possible · dynamic assumptions; the judgment Σ : Γ ⊢ Ar = A : o, whose definition we omit and refer to the judgmental version in =-=[22]-=-), denotes higher-order unification. Σ : Γ −→ G Program Γ under signature Σ uniformly entails goal G. Σ : Γ D −→ A Focused clause D from Γ under signature Σ entails atom A. We remark that the backchai... |

8 | Object Calculi in Linear Logic
- Bugliesi, Delzanno, et al.
(Show Context)
Citation Context ...tiset rewriting to encode aspects of planning and concurrency [15, 18]. More developed research was concerned with finding a logical counterpart of object-based languages such as the Object Calculus; =-=[16]-=- introduced Ob⊸, an object language where methods are represented as logical formulae and whose operational semantics is realized via proof search. The language is then encoded in a linear extension o... |

7 |
M.: Model checking linear logic specifications. TPLP
- Bozzano, Delzanno, et al.
- 2004
(Show Context)
Citation Context ...s [3]. This yielded an approach to model-checking where verifying a safety problem encoded in temporal logic is akin to computing the fixed point of a linear logic program. This is further studied in =-=[14]-=-, where bottom-up evaluation is extended to first order LO programs with universally quantified goals and possibly empty heads. See for more details the Chapter [29] in this volume. We remark that bot... |

4 |
behold! Concurrent structured processes
- LO
- 1990
(Show Context)
Citation Context ...ombinator in a language such as Standard ML: Example 2. mappred(P,[],[]). mappred(P,[X|Xs],[Y|Ys]) :- P(X,Y), mappred(P,Xs,Ys). A sample goal could be P = (lambda x y\ reverse(x,y)), mappred(P,[[1,2],=-=[3,4]-=-],Ys). with answer substitution Ys = [[2,1],[4,3]]. ⋄ Although some nifty applications based on these features emerged early on, e.g. [32], predicate-as-values, we argue, never managed to attain the s... |

4 | A proposal for modules in λProlog
- Miller
- 1994
(Show Context)
Citation Context ...roduction of “impure”, i.e. extra-logical, features, such as cut, negation-as-failure or assert/retract. This outcome is not specific to LP and has been named “recreating the Turing Machine” syndrome =-=[48]-=-: starting from a computationally clean and semantically motivated language, one tends to add external mechanisms in order to make it suitable for programming-in-the-large. This inevitably tends to cl... |

3 | Proofs as computations in linear logic
- DELZANNO, MARTELLI
- 1987
(Show Context)
Citation Context ... formulae and whose operational semantics is realized via proof search. The language is then encoded in a linear extension of second-order N-Prolog, with a limited form of predicate quantification In =-=[30]-=- the authors present a restriction of Forum with the aim of integrating logic programming with the rewrite-based specification languages; intended applications are modelling of concurrent systems and ... |

3 | Concurrent and Reactive Constraint Programming, in "A 25-Year Perspective on Logic Programming
- GABBRIELLI, PALAMIDESSI, et al.
(Show Context)
Citation Context ...ng clause heads to multisets of atoms connected by multiplicative disjunction (�), i.e. clauses have the form G ⊸ A1�,...,�An The starting point was the family of concurrent LP languages (see Chapter =-=[35]-=- in this volume) as a way to provide a logical account of object-oriented computations: objects are viewed as AND-concurrent, stream-communicating via shared variables (proof) processes, where the arg... |

2 |
On the Relations between Disjunctive and Linear Logic Programming
- Bozzano, Delzanno, et al.
- 2001
(Show Context)
Citation Context ...zanno’s thesis [28, 38]. The latter then moved to Genoa, where he collaborated with M. Martelli, Bozzano and others. The relationship between linear and disjunctive LP mentioned in [4] is taken up in =-=[12]-=-, where the authors show that LO can be seen as a sub-structural fragments of DLP, where contraction on the right is disallowed. More extensive connections betweena fragment of LO and DLP are further... |

2 |
Expressiveness of the abstract logic programming language Forum in planning and concurrency
- Bruscoli, Guglielmi
- 1994
(Show Context)
Citation Context ... a monadic modality encapsulating synchronous connectives. 3.4 Forum Some early work exploited the connection between linear logic and multiset rewriting to encode aspects of planning and concurrency =-=[15, 18]-=-. More developed research was concerned with finding a logical counterpart of object-based languages such as the Object Calculus; [16] introduced Ob⊸, an object language where methods are represented ... |

2 |
and Gaetano Aurelio Lanzarone, A metalogic programming language
- Costantini
- 1989
(Show Context)
Citation Context ...schi then hooked up with Andreoli to develop LO as we have mentioned in Section 2.3. Miller also supervised Arcelli’s thesis [6] in Milano, where she related second-order λProlog to Reflective Prolog =-=[27]-=-. She and coauthors went on investigating applications of the language for example to program transformations [7]. Independently, Momigliano [52] extended Miller’s [46], providing a way of encoding vi... |

2 | editors. Twenty-five Years of Logic Programming in Italy, volume 6000 - Dovier, Pontelli - 1993 |

2 |
N.: Combining negation as failure and embedded implications in logic programs
- Giordano, Olivetti
- 1998
(Show Context)
Citation Context ... applications w.r.t. modules and scoping constructs and extension to modal analysis, see e.g. [9]. We will not analyze this further as already well detailed in [17]. We will, however, briefly mention =-=[37]-=- that fixes some of the problems raised in [33]. The authors propose an operational semantics extending Stärk’s ESLDNF, establishing a soundness and completeness for non-floundering queries is with re... |

1 |
Tiziana Castagnetti, and Remo Pareschi. Abstract interpretation of linear logic programming
- Andreoli
- 1993
(Show Context)
Citation Context ...ombinator in a language such as Standard ML: Example 2. mappred(P,[],[]). mappred(P,[X|Xs],[Y|Ys]) :- P(X,Y), mappred(P,Xs,Ys). A sample goal could be P = (lambda x y\ reverse(x,y)), mappred(P,[[1,2],=-=[3,4]-=-],Ys). with answer substitution Ys = [[2,1],[4,3]]. ⋄ Although some nifty applications based on these features emerged early on, e.g. [32], predicate-as-values, we argue, never managed to attain the s... |

1 |
Aspetti di ordine superiore e di metalivello della programmazione logica
- Arcelli
- 1991
(Show Context)
Citation Context ...in linguistic theories, e.g. the rendering of filler-gap dependencies. Pareschi then hooked up with Andreoli to develop LO as we have mentioned in Section 2.3. Miller also supervised Arcelli’s thesis =-=[6]-=- in Milano, where she related second-order λProlog to Reflective Prolog [27]. She and coauthors went on investigating applications of the language for example to program transformations [7]. Independe... |

1 |
F.: Implementing higher-order term-rewriting for program transformation in λProlog
- Arcelli, Formato
(Show Context)
Citation Context ...i’s thesis [6] in Milano, where she related second-order λProlog to Reflective Prolog [27]. She and coauthors went on investigating applications of the language for example to program transformations =-=[7]-=-. Independently, Momigliano [52] extended Miller’s [46], providing a way of encoding via the double negation translation of all classical logic into a focused uniform system. The language was FOHF, bu... |

1 |
M.C.: Theoretical Foundations and Semantics
- Bossi, Meo
- 2010
(Show Context)
Citation Context ...gic Programming 255 (and somewhat worn out) example is again the logical foundations of negation. More in general, it is by now usual to contrast the traditional model-theoretic approach (see Chapter =-=[11]-=- in this volume) to the proof-theoretic one, which “happens” to be at the core of most of the work about higher-order extensions of logic programming. Arguably, many theoretical developments in logic ... |

1 | F.: Static Analysis, Abstract Interpretation and Verification in (Constraint Logic) Programming
- Delzanno, Giacobazzi, et al.
- 2010
(Show Context)
Citation Context ...rogram. This is further studied in [14], where bottom-up evaluation is extended to first order LO programs with universally quantified goals and possibly empty heads. See for more details the Chapter =-=[29]-=- in this volume. We remark that bottom-up evaluation has now gained an important role in general sequent-based automated theorem proving [42, 25], as well as in the operational semantics of LolliMon [... |